A109976 Diagonal sums of number triangle A109974.

1, 2, 3, 6, 7, 16, 19, 46, 66, 159, 274, 667, 1320, 3263, 7156, 18084, 42794, 111018, 278752, 743889, 1959482, 5383395, 14761634, 41740307, 118517301, 344580865, 1009349749, 3013665637, 9081346743, 27808754039, 86015003997, 269796018547

Offset: 0

Author

Paul Barry, Jul 06 2005

Keywords

• easy
• nonn

Links

• Robert Israel, Table of n, a(n) for n = 0..1063

Crossrefs

Cf. A109974

Programs

Maple

f:= n -> add(numtheory:-sigma[k](n-2*k+1),k=0..n/2):
map(f, [$0..50]); # Robert Israel, May 25 2018

Mathematica

Array[Sum[DivisorSigma[k, (# - 2 k + 1)], {k, 0, Floor[#/2]}] &, 32, 0] (* Michael De Vlieger, May 27 2018 *)

Formula

a(n) = Sum_{k=0..floor(n/2)} sigma_k(n-2k+1). - Corrected by Robert Israel, May 25 2018

G.f.: Sum_{n>=1} x^(n-1)/((1-x^n)*(1-n*x^2)). - Robert Israel, May 27 2018