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

0,3

Links

Table of n, a(n) for n=0..39.

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.

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 *)

Prog

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

Crossrefs

Cf. A000010, A121775.

Sequence in context: A011913 A024531 A034198 * A310085 A310086 A310087

Adjacent sequences: A121773 A121774 A121775 * A121777 A121778 A121779

Keyword

nonn

Author

Paul D. Hanna, Aug 23 2006

Status

approved