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A278969
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Number of 7-digit numbers whose sum of digits is n.
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5
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1, 7, 28, 84, 210, 462, 924, 1716, 3003, 5004, 7995, 12306, 18312, 26418, 37038, 50568, 67353, 87648, 111573, 139068, 169863, 203463, 239148, 275988, 312873, 348558, 381723, 411048, 435303, 453438, 464653, 468448, 464653, 453438, 435303, 411048, 381723, 348558, 312873, 275988, 239148, 203463, 169863, 139068, 111573, 87648, 67353, 50568, 37038, 26418, 18312, 12306, 7995, 5004, 3003, 1716, 924, 462, 210, 84, 28, 7, 1
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OFFSET
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1,2
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COMMENTS
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There are 9000000 numbers with 7 decimal digits, the smallest being 1000000 and the largest 9999999.
Differs for n >= 10 (5004 vs 5005) from A000579(n+5) = binomial(n+5,6). - M. F. Hasler, Mar 05 2017
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LINKS
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Table of n, a(n) for n=1..63.
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FORMULA
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G.f.: (x - x^10)/(1 - x)*((1 - x^10)/(1 - x))^6. - Michael De Vlieger, Dec 07 2016
a(64-n) = a(n), 1 <= n <= 63. - M. F. Hasler, Mar 05 2017
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EXAMPLE
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a(2)=7: 1000001, 1000010, 1000100, 1001000, 1010000, 1100000, 2000000.
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MATHEMATICA
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Rest@ CoefficientList[Series[(x - x^10)/(1 - x) ((1 - x^10)/(1 - x))^#, {x, 0, 9 (# + 1)}], x] &@ 6 (* or *)
Function[w, Count[w, #] & /@ Range[Max@ w]]@ Map[Total@ IntegerDigits@ # &, Range[10^#, 10^(# + 1) - 1]] &@ 6 (* Michael De Vlieger, Dec 07 2016 *)
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PROG
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(PARI) b=vector(63, i, 0); for(n=1000000, 9999999, a=eval(Vec(Str(n))); b[sum(j=1, 7, a[j])]++); for(n=1, 63, print1(b[n], ", "))
(PARI) Vec((1-x^9)*(1-x^10)^6/(1-x)^7) \\ shorter than (1-x^9)/(1-x)*((1-x^10)/(1-x))^6, but not better. - M. F. Hasler, Mar 05 2017
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CROSSREFS
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A071817 (3-digit numbers), A090579 (4-digit numbers), A090580 (5-digit numbers), A090581 (6-digit numbers), A278971 (8-digit numbers).
Sequence in context: A008489 A023032 A341204 * A000579 A290994 A049017
Adjacent sequences: A278966 A278967 A278968 * A278970 A278971 A278972
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KEYWORD
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base,fini,full,nonn,easy
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AUTHOR
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Daniel Mondot, Dec 02 2016
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STATUS
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approved
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