A110051 Expansion of (1-x+2*x^3+x^2)/((1-x)*(2*x+1)*(2*x-1)*(4*x^2+4*x-1)).

1, 4, 25, 119, 599, 2887, 14039, 67767, 327607, 1581751, 7638967, 36883895, 178097591, 859930039, 4152135095, 20048276919, 96801746359, 467400158647, 2256808013239, 10896832949687, 52614565424567, 254045594545591

Offset

0,2

Links

Table of n, a(n) for n=0..21.

Index entries for linear recurrences with constant coefficients, signature (5, 4, -24, 0, 16).

Formula

a(0)=1, a(1)=4, a(2)=25, a(3)=119, a(4)=599, a(n)=5*a(n-1)+4*a(n-2)- 24*a(n-3)+ 16*a(n-5). - Harvey P. Dale, Sep 07 2012

a(n)=1/112*(-2*(7*(-2)^n+7*2^(n+1)-8)+(13-9*Sqrt[2])*(2-2*Sqrt[2])^n+ 9* 2^(n+1/2)*(1+Sqrt[2])^n+13*(2*(1+Sqrt[2]))^n). - Harvey P. Dale, Sep 07 2012

Maple

seriestolist(series((1-x+2*x^3+x^2)/((1-x)*(2*x+1)*(2*x-1)*(4*x^2+4*x-1)), x=0, 25)); -or- Floretion Algebra Multiplication Program, FAMP Code: -basejrokseq[A*B] with A = + 'i - .5'j + .5'k - .5j' + .5k' - 'ii' - .5'ij' - .5'ik' - .5'ji' - .5'ki' and B = - .5'i + .5'j + 'k - .5i' + .5j' - 'kk' - .5'ik' - .5'jk' - .5'ki' - .5'kj'; RokType: Y[15] = Y[15] + 1/2

Mathematica

CoefficientList[Series[(1-x+2x^3+x^2)/((1-x)(2x+1) (2x-1) (4x^2+4x-1)), {x, 0, 30}], x] (* or *) LinearRecurrence[{5, 4, -24, 0, 16}, {1, 4, 25, 119, 599}, 30] (* Harvey P. Dale, Sep 07 2012 *)

Crossrefs

Cf. A110050, A110052.

Sequence in context: A070764 A327646 A244746 * A334551 A273023 A013187

Adjacent sequences: A110048 A110049 A110050 * A110052 A110053 A110054

Keyword

easy,nonn

Author

Creighton Dement, Jul 10 2005

Status

approved