A178078 Sequence with a (1,-1) Somos-4 Hankel transform.

1, 0, 1, 1, 4, 12, 42, 147, 527, 1914, 7039, 26159, 98110, 370919, 1412211, 5410273, 20841886, 80685792, 313747624, 1224895416, 4799435482, 18867423751, 74394859297, 294152650731, 1166021396660, 4632969618849, 18448290723435

Offset

0,5

Comments

Hankel transform is A178079.

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Paul Barry, Integer sequences from elliptic curves, arXiv:2306.05025 [math.NT], 2023.

Formula

a(n) = Sum_{k=0..floor(n/2)} ( (C(n-k,k)/(n-2k+1))*Sum_{i=0..k} C(k,i)*C(n-k-i-1,n-2*k-i)*3^(n-2*k-i)*(-2)^i*1^(k-i) ).

Mathematica

Table[Sum[(Binomial[n-k, k]/(n-2*k+1))*Sum[Binomial[k, j]*Binomial[n-k-j-1, n-2*k-j]*3^(n-2*k-j)*(-2)^j*1^(k-j), {j, 0, k}], {k, 0, Floor[n/2]}] + ((1 + (-1)^n)*(2/3)^(n/2))/2, {n, 0, 50}]  (* G. C. Greubel, Sep 18 2018 *)

Prog

(PARI) a(n) = sum(k=0, floor(n/2), sum(j=0, k, (binomial(n-k, k)/(n-2*k+1)) *binomial(k, j)*binomial(n-k-j-1, n-2*k-j)*3^(n-2*k-j)*(-2)^j));
for(n=0, 50, print1(a(n), ", ")) \\ G. C. Greubel, Sep 18 2018

Crossrefs

Sequence in context: A052303 A017942 A149344 * A135489 A100217 A149345

Adjacent sequences: A178075 A178076 A178077 * A178079 A178080 A178081

Keyword

easy,nonn

Author

Paul Barry, May 19 2010

Status

approved