A109784 Expansion of (x^2-x-1)*(x^3-x^2+x-2) / ((x-1)*(2*x-1)*(x^2+x+1)*(x^2+1)).

2, 5, 6, 14, 31, 59, 118, 238, 475, 951, 1902, 3802, 7607, 15215, 30426, 60854, 121711, 243419, 486838, 973678, 1947355, 3894711, 7789422, 15578842, 31157687, 62315375, 124630746, 249261494, 498522991, 997045979, 1994091958, 3988183918

Offset

0,1

Comments

Floretion Algebra Multiplication Program, 2ibasesumseq[5'i + .5i' + .5'ii' + .5'jj' + .5'kk' + .5e], sumtype: default (ver. f). Note: Due to FAMP's limited ability to handle large numbers, it is unclear if 2ibasesumseq and (a(n)) continue to coincide for large n.

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (2,-1,3,-2,1,-2).

Formula

a(n) = 2*a(n-1) - a(n-2) + 3*a(n-3) - 2*a(n-4) + a(n-5) - 2*a(n-6) for n>5. - Colin Barker, May 15 2019

Mathematica

LinearRecurrence[{2, -1, 3, -2, 1, -2}, {2, 5, 6, 14, 31, 59}, 40] (* Harvey P. Dale, Nov 28 2019 *)

Prog

(PARI) Vec((1 + x - x^2)*(2 - x + x^2 - x^3) / ((1 - x)*(1 - 2*x)*(1 + x^2)*(1 + x + x^2)) + O(x^40)) \\ Colin Barker, May 15 2019

Crossrefs

Sequence in context: A275839 A057302 A237352 * A221472 A076624 A205385

Adjacent sequences: A109781 A109782 A109783 * A109785 A109786 A109787

Keyword

nonn,easy

Author

Creighton Dement, Aug 14 2005

Status

approved