A121776 Antidiagonal sums of triangle A121775.

1, 1, 3, 6, 10, 16, 23, 36, 52, 76, 118, 181, 271, 427, 675, 1057, 1686, 2705, 4318, 6923, 11142, 17966, 28999, 46793, 75522, 122018, 197254, 318907, 515616, 833796, 1348542, 2181304, 3528487, 5707947, 9234075, 14938991, 24169111, 39103056, 63265607, 102359886

Offset: 0

Author

Paul D. Hanna, Aug 23 2006

Keywords

• nonn

Crossrefs

Cf. A000010, A121775.

Programs

Mathematica

a[0] = 1; a[n_] := Sum[DivisorSum[n-k, EulerPhi[(n-k)/#] * Binomial[#, k] &], {k, 0, Floor[n/2]}]; Array[a, 50, 0] (* Amiram Eldar, Aug 15 2023 *)

PARI

a(n)=if(n==0,1,sum(k=0,n\2,sumdiv(n-k,d,eulerphi((n-k)/d)*binomial(d,k))))

Formula

a(n) = Sum_{k=0..[n/2]} Sum_{d|(n-k)} phi((n-k)/d)*C(d,k) for n>0, with a(0)=1.