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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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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
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OFFSET
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0,2
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COMMENTS
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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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G. E. Andrews, Number Theory, 1971, Dover Publications New York, p. 44, p. 201-207.
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LINKS
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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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Triangle begins
{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 = CoefficientList[Series[1 + 4*Sum[(-1)^(1 + n)/(-1 + x^(1 - 2*n)), {n, 100}], {x, 0, 100}], x]; 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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KEYWORD
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AUTHOR
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STATUS
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approved
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