A167478 Expansion of (1-2x+6x^2-x^3)/(1-3x+x^2)^2.

1, 4, 19, 75, 264, 869, 2741, 8396, 25175, 74271, 216336, 623689, 1782889, 5060500, 14277019, 40070259, 111954456, 311555501, 863978525, 2388417116, 6584117471, 18104432199, 49667825184, 135974484625, 371543306449, 1013443026724

Offset: 0

Author

Paul Barry, Nov 04 2009

Keywords

• easy
• nonn

Comments

Hankel transform of A054109.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (6,-11,6,-1).

Crossrefs

Cf. A054109.

Programs

Mathematica

LinearRecurrence[{6, -11, 6, -1}, {1, 4, 19, 75}, 100] (* G. C. Greubel, Jun 13 2016 *)
CoefficientList[Series[(1-2x+6x^2-x^3)/(1-3x+x^2)^2,{x,0,30}],x] (* Harvey P. Dale, Aug 04 2018 *)

Formula

G.f.: (1-2*x+6*x^2-x^3)/(1-3*x+x^2)^2.

a(n) = 6*a(n-1) - 11*a(n-2) + 6*a(n-3) - a(n-4). - Wesley Ivan Hurt, Jul 28 2022