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A192928
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The Gi1 and Gi2 sums of Losanitsch’s triangle A034851
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6
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1, 1, 1, 1, 2, 2, 3, 3, 5, 6, 9, 11, 16, 20, 29, 37, 53, 69, 98, 130, 183, 245, 343, 463, 646, 877, 1220, 1664, 2310, 3161, 4381, 6009, 8319, 11430, 15811, 21751, 30070, 41405, 57216, 78836, 108906, 150130, 207346
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OFFSET
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0,5
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COMMENTS
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The Gi1 and Gi2 sums, see A180662 for their definitions, of Losanitsch's triangle A034851 equal this sequence.
From Johannes W. Meijer, Aug 26 2013: (Start)
The a(n) are also the Ca1 and Ca2 sums of McGarvey’s triangle A102541.
Furthermore they are the Kn11 and Kn12 sums of triangle A228570.
And finally the terms of this sequence are the row sums of triangle A228572. (End)
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LINKS
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Table of n, a(n) for n=0..42.
R. J. Mathar, Paving rectangular regions with rectangular tiles,...., arXiv:1311.6135 [math.CO], Table 25.
Index entries for linear recurrences with constant coefficients, signature (1,1,-1,1,0,-1,0,1,-1,0,0,-1).
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FORMULA
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G.f.: (-1/2)*(1/(x^4+x-1) + (1+x+x^4)/(x^8+x^2-1))= -(1+x)*(x^7-x^6+x^5+x-1) / ( (x^4+x-1)*(x^8+x^2-1) ).
a(n) = (A003269(n+1)+x(n)+x(n-1)+x(n-4))/2 with x(2*n) = A003269(n+1) and x(2*n+1) = 0.
From Johannes W. Meijer, Aug 26 2013: (Start)
a(n) = sum(A228572(n, k), k=0..n)
a(n) = sum(A228570(n-k, k), k=0..floor(n/2))
a(n) = sum(A102541(n-2*k, k), k=0..floor(n/3))
a(n) = sum(A034851(n-3*k, k), k=0..floor(n/4)) (End)
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MAPLE
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A192928 := proc(n): (A003269(n+1)+x(n)+x(n-1)+x(n-4))/2 end: A003269 := proc(n): sum(binomial(n-1-3*j, j), j=0..(n-1)/3) end: x:=proc(n): if type(n, even) then A003269(n/2+1) else 0 fi: end: seq(A192928(n), n=0..42);
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CROSSREFS
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Cf. A003269, A034851, A102541, A180662, A228570, A228572.
Sequence in context: A240201 A020999 A079955 * A136417 A130791 A133277
Adjacent sequences: A192925 A192926 A192927 * A192929 A192930 A192931
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KEYWORD
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nonn,easy
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AUTHOR
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Johannes W. Meijer, Jul 14 2011
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STATUS
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approved
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