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A141666
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).
1
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
OFFSET
0,2
COMMENTS
Row sums are {1, 8, 24, 32, 24, 48, 96, 64, 24, 104, 144}.
REFERENCES
G. E. Andrews, Number Theory, 1971, Dover Publications New York, p. 44, p. 201-207.
LINKS
Eric Weisstein's World of Mathematics, Sum of Squares Function
FORMULA
t(n,m) = r2(n-m+1)*r2(m+1).
EXAMPLE
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}
MATHEMATICA
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
CROSSREFS
Cf. A004018.
Sequence in context: A245517 A179526 A098525 * A102127 A201625 A223824
KEYWORD
nonn,tabl
AUTHOR
STATUS
approved