A125094 Eigensequence of A061554 regarded as a triangle: a(n) = Sum_{k=0..n-1} A061554(n-1,k)*a(k) with a(0)=1.

1, 1, 2, 5, 13, 36, 104, 313, 977, 3152, 10486, 35880, 126039, 453725, 1671322, 6291148, 24170312, 94680426, 377788108, 1534169595, 6335718925, 26589240583, 113323479393, 490203781505, 2150975413846, 9569147610181, 43140286838567

Offset

0,3

Links

Table of n, a(n) for n=0..26.

Formula

a(n) = Sum_{k=0..n-1} a(k)*C(n-1, floor[n/2 - (-1)^(n-k-1)*(k+1)/2] ).

Example

a(4) = 3*(1) + 3*(1) + 1*(2) + 1*(5) = 13.
a(5) = 6*(1) + 4*(1) + 4*(2) + 1*(5) + 1*(13) = 36.
a(6) = 10*(1) + 10*(1) + 5*(2) + 5*(5) + 1*(13) + 1*(36) = 104.
Triangle version of A061554 begins:
1;
1, 1;
2, 1, 1;
3, 3, 1, 1;
6, 4, 4, 1, 1;
10, 10, 5, 5, 1, 1; ...

Prog

(PARI) {a(n)=if(n==0, 1, sum(k=0, n-1, a(k)*binomial(n-1, n\2+(-1)^(n-k)*((k+1)\2))))}

Crossrefs

Cf. A061554.

Sequence in context: A136751 A154836 A087626 * A271941 A114465 A135310

Adjacent sequences: A125091 A125092 A125093 * A125095 A125096 A125097

Keyword

nonn

Author

Paul D. Hanna, Nov 20 2006

Status

approved