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%I #6 Jun 03 2021 03:20:32
%S 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,
%T -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,
%U 10,-8,10,-10,11,-10,11,-9,11,-11,12,-11,12,-10,12,-12,13,-12,13,-11,13,-13
%N Diagonal sums of number triangle A117446.
%H G. C. Greubel, <a href="/A117448/b117448.txt">Table of n, a(n) for n = 0..1000</a>
%F 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.
%t Table[Sum[Binomial[JacobiSymbol[k, 3], n-2*k], {k, 0, Floor[n/2]}], {n, 0, 80}] (* _G. C. Greubel_, Jun 02 2021 *)
%o (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
%Y Cf. A117446, A117447.
%K easy,sign
%O 0,7
%A _Paul Barry_, Mar 16 2006
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