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Search: id:A141666
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| A141666 |
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A symmetrical triangle of coefficients based on A004018 (or number of ways of writing n as a sum of 2 squares): t(n,m)=r2(n-m+1)*r2(m+1). |
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+0
1
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| 1, 4, 4, 4, 16, 4, 0, 16, 16, 0, 4, 0, 16, 0, 4, 8, 16, 0, 0, 16, 8, 0, 32, 16, 0, 16, 32, 0, 0, 0, 32, 0, 0, 32, 0, 0, 4, 0, 0, 0, 16, 0, 0, 0, 4, 4, 16, 0, 0, 32, 32, 0, 0, 16, 4, 8, 16, 16, 0, 0, 64, 0, 0, 16, 16, 8
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Row sums are:
{1, 8, 24, 32, 24, 48, 96, 64, 24, 104, 144}.
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REFERENCES
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http : // mathworld.wolfram.com/SumofSquaresFunction.html
G. E. Andrews, Number Theory, 1971, Dover Publications New York, p 44,p 201-207.
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FORMULA
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t(n,m)=r2(n-m+1)*r2(m+1).
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EXAMPLE
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{1},
{4, 4},
{4, 16, 4},
{0, 16, 16, 0},
{4, 0, 16, 0, 4},
{8, 16, 0, 0, 16, 8},
{0, 32, 16, 0, 16, 32, 0},
{0, 0, 32, 0, 0, 32, 0, 0},
{4, 0, 0, 0, 16, 0, 0, 0, 4},
{4, 16, 0, 0, 32, 32, 0, 0, 16, 4},
{8, 16, 16, 0, 0, 64, 0, 0, 16, 16, 8}
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MATHEMATICA
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Clear[a] a = Table[SeriesCoefficient[Series[1 + 4Sum[(-1)^(1 + n)/(-1 + x^(1 - 2*n)), {n, 100}], {x, 0, 100}], n], {n, 0, 100}]; Table[Table[a[[n - m + 1]]*a[[m + 1]], {m, 0, n}], {n, 0, 10}]; Flatten[%]
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CROSSREFS
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Cf. A004018.
Sequence in context: A151906 A151896 A098525 this_sequence A102127 A131946 A034896
Adjacent sequences: A141663 A141664 A141665 this_sequence A141667 A141668 A141669
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KEYWORD
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nonn,uned
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AUTHOR
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Roger L. Bagula and Gary W. Adamson (rlbagulatftn(AT)yahoo.com), Sep 05 2008
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