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A174959
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G.f.: x^3*(2*x-1) / ((1-x)*(1-x-x^2)*(1-2*x^2)).
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1
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0, 0, 0, -1, 0, -2, 1, -2, 6, 3, 24, 26, 81, 106, 250, 355, 732, 1086, 2073, 3158, 5742, 8899, 15664, 24562, 42273, 66834, 113202, 180035, 301428, 481462, 799273, 1280734, 2112774, 3393507, 5571816, 8965322, 14668209, 23633530, 38563882, 62197411, 101285580
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OFFSET
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0,6
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REFERENCES
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Burton, David M., Elementary number theory, McGraw Hill, N.Y., 2002, p. 286
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LINKS
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Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (2,2,-5,0,2).
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FORMULA
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a(n) = Sum_{j=0..floor((n-1)/2)} (-2^j + binomial(n-j-1, j)).
a(n) = Fibonacci(n+1) - 2^ceiling(n/2) - 1.
a(n) = A000045(n+1) - A016116(n+1) - 1.
a(n) = 2*a(n-1) + 2*a(n-2) - 5*a(n-3) + 2*a(n-5) for n^5. - Colin Barker, Dec 01 2019
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MATHEMATICA
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Table[Sum[-2^(j) +
Binomial[n - j - 1, j], {j, 0, Floor[(n - 1)/2]}], {n, 0, 30}]
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PROG
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(PARI) concat([0, 0, 0], -Vec(x^3*(1 - 2*x) / ((1 - x)*(1 - x - x^2)*(1 - 2*x^2)) + O(x^40))) \\ Colin Barker, Dec 01 2019
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CROSSREFS
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Sequence in context: A269223 A121341 A241737 * A126093 A065279 A343383
Adjacent sequences: A174956 A174957 A174958 * A174960 A174961 A174962
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KEYWORD
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sign,easy
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AUTHOR
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Roger L. Bagula, Dec 02 2010
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EXTENSIONS
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More terms from Colin Barker, Dec 01 2019
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STATUS
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approved
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