A106157 Expansion of g.f. (1-x-x^3+x^4-2*x^2)/((1-2*x)*(x-1)^2*(x+1)^2).

-1, -1, -2, -1, -2, 1, 2, 11, 22, 53, 106, 223, 446, 905, 1810, 3635, 7270, 14557, 29114, 58247, 116494, 233009, 466018, 932059, 1864118, 3728261, 7456522, 14913071, 29826142, 59652313, 119304626, 238609283, 477218566, 954437165, 1908874330, 3817748695, 7635497390, 15270994817

Offset

0,3

Comments

The sequence reveals itself to a degree upon factorization: (-1, -1, -(2), -1, -(2), 1, (2), (11), (2)*(11), (53), (2)*(53), (223), (2)*(223), (5)*(181), (2)*(5)*(181), (5)*(727), (2)*(5)*(727), (14557), (2)*(14557), (7)*(53)*(157), (2)*(7)*(53)*(157), (7)*(33287), (2)*(7)*(33287), (17)*(109)*(503), (2)*(17)*(109)*(503), (1429)*(2609), (2)*(1429)*(2609), (97)*(153743), (2)*(97)*(153743), (7)*(8521759),) with a(n+1)/a(n) apparently approaching 2 and a(2n)/a(2n-1) = 2 for all n > 0.

Floretion Algebra Multiplication Program, FAMP Code: 1vesrokseq[A*B] with A = + 'ii' + .5'jj' + .5'kk' + .5'ij' + .5'ik' + .5'ji' + 'jk' + .5'ki' + 'kj', B = + .25'i + .25i' + .25'ii' + .25'jj' + .25'kk' + .25'jk' + .25'kj' + .25e and RokType: Y[15] = Y[15] - p (internal program code)

Links

Table of n, a(n) for n=0..37.

Index entries for linear recurrences with constant coefficients, signature (2,2,-4,-1,2).

Formula

a(n) = (1/18)*(2^(n+1) - (3n+2)(-1)^n - 9n - 18).

Mathematica

LinearRecurrence[{2, 2, -4, -1, 2}, {-1, -1, -2, -1, -2}, 40] (* Harvey P. Dale, Mar 29 2023 *)

Crossrefs

Sequence in context: A083273 A353398 A193163 * A181816 A113738 A287854

Adjacent sequences: A106154 A106155 A106156 * A106158 A106159 A106160

Keyword

sign,easy

Author

Creighton Dement, May 08 2005

Status

approved