A294035 a(n) = 3^n*hypergeom([-n/3, (1-n)/3, (2-n)/3], [1, 1], -1).

1, 3, 9, 33, 153, 783, 4059, 21087, 110889, 592899, 3214989, 17608077, 97150491, 539331237, 3010588317, 16887545793, 95134584969, 537942476907, 3051902823849, 17365639042449, 99076018204413, 566622950463099, 3247670747106927, 18651711493531539, 107315246617831179

Offset

0,2

Comments

Diagonal of rational function 1/(1 - (x^3 + y^3 + z^3 + 3*x*y*z)). - Gheorghe Coserea, Aug 04 2018

Links

Robert Israel, Table of n, a(n) for n = 0..1288

Formula

Let H(m, n, x) = m^n*hypergeom([(k-n)/m for k=0..m-1], [1 for k=0..m-2], x) then a(n) = H(3, n, -1).

a(n) ~ sqrt(3) * 6^n / (Pi*n) . - Vaclav Kotesovec, Nov 02 2017

-(54*(n+2))*(n+1)*a(n)+27*(n+2)^2*a(n+1)-(3*(3*n^2+15*n+19))*a(n+2)+(n+3)^2*a(n+3) = 0. - Robert Israel, Nov 02 2017

Maple

T := (m, n, x) -> m^n*hypergeom([seq((k-n)/m, k=0..m-1)], [seq(1, k=0..m-2)], x):
seq(simplify(T(3, n, -1)), n=0..39);

Mathematica

Table[3^n * HypergeometricPFQ[{-n/3, (1 - n)/3, (2 - n)/3}, {1, 1}, -1], {n, 0, 30}] (* Vaclav Kotesovec, Nov 02 2017 *)

Crossrefs

H(1, n, 1) = A000007(n), H(2, n, 1) = A000984(n), H(3, n, 1) = A006077(n), H(4, n, 1) = A294036(n), H(1, n, -1) = A000079(n), H(2, n, -1) = A098335(n), H(3, n, -1) = this seq., H(4, n, -1) = A294037(n).

Sequence in context: A180632 A279840 A009220 * A007489 A294638 A201968

Adjacent sequences: A294032 A294033 A294034 * A294036 A294037 A294038

Keyword

nonn

Author

Peter Luschny, Nov 02 2017

Status

approved