A181655 Expansion of (1+2x-x^3+x^4)/(1-4x^2+3x^4).

1, 2, 4, 7, 14, 22, 44, 67, 134, 202, 404, 607, 1214, 1822, 3644, 5467, 10934, 16402, 32804, 49207, 98414, 147622, 295244, 442867, 885734, 1328602, 2657204, 3985807, 7971614, 11957422, 23914844, 35872267, 71744534, 107616802, 215233604

Offset: 0

Author

Paul Barry, Nov 03 2010

Keywords

• easy
• nonn

Comments

Row sums of A181654.

Links

• Index entries for linear recurrences with constant coefficients, signature (0,4,0,-3).

Crossrefs

Cf. A060816, A198643 (bisections).

Programs

Mathematica

CoefficientList[Series[(1+2x-x^3+x^4)/(1-4x^2+3x^4),{x,0,40}],x] (* or *) Join[{1},LinearRecurrence[{0,4,0,-3},{2,4,7,14},40]] (* Harvey P. Dale, Jan 11 2012 *)

PARI

A181655(n)=if(bitand(n,1), 3^(n\2)*5\2, n, 3^(n\2-1)*5-1, 1) \\ M. F. Hasler, Apr 06 2019

Formula

G.f.: (1+2*x-x^3+x^4)/((1-x^2)*(1-3*x^2)).

a(n) = 5*A038754(n+1)/6 - A040001(n)/2. - R. J. Mathar, May 14 2016

a(2n-1) = A060816(n-1), a(2n) = A198643(n-1); n >= 1. a(n+1) = 2*a(n) if n is odd. - M. F. Hasler, Apr 06 2019