A117448 - OEIS

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A117448

Diagonal sums of number triangle A117446.

1, 0, 1, 1, 1, -1, 2, -1, 2, 0, 2, -2, 3, -2, 3, -1, 3, -3, 4, -3, 4, -2, 4, -4, 5, -4, 5, -3, 5, -5, 6, -5, 6, -4, 6, -6, 7, -6, 7, -5, 7, -7, 8, -7, 8, -6, 8, -8, 9, -8, 9, -7, 9, -9, 10, -9, 10, -8, 10, -10, 11, -10, 11, -9, 11, -11, 12, -11, 12, -10, 12, -12, 13, -12, 13, -11, 13, -13

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OFFSET

0,7

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

FORMULA

a(n) = Sum_{k=0..floor(n/2)} binomial(L(k/3), n-2k), where L(j/p) is the Legendre symbol of j and p.

MATHEMATICA

Table[Sum[Binomial[JacobiSymbol[k, 3], n-2*k], {k, 0, Floor[n/2]}], {n, 0, 80}] (* G. C. Greubel, Jun 02 2021 *)

PROG

(Sage) [sum( binomial(kronecker(k, 3), n-2*k) for k in (0..n//2) ) for n in (0..80)] # G. C. Greubel, Jun 02 2021

CROSSREFS