A110062 Expansion of (1 - x + 2*x^2) / (1 - x^3 + x^4).

1, -1, 2, 1, -2, 3, -1, -3, 5, -4, -2, 8, -9, 2, 10, -17, 11, 8, -27, 28, -3, -35, 55, -31, -32, 90, -86, -1, 122, -176, 85, 123, -298, 261, 38, -421, 559, -223, -459, 980, -782, -236, 1439, -1762, 546, 1675, -3201, 2308, 1129, -4876, 5509, -1179, -6005, 10385, -6688, -4826, 16390, -17073, 1862, 21216

Offset: 0

Author

Creighton Dement, Jul 10 2005

Keywords

• easy
• sign

Comments

One of several sequences which appear to "spiral outwards" when plotted against each other (see A110061-A110064).

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (0,0,1,-1).

Crossrefs

Cf. A110061, A110063, A110064.

Programs

Maple

seriestolist(series((1-x+2*x^2)/(1-x^3+x^4), x=0,60)); -or- Floretion Algebra Multiplication Program, FAMP Code: 4ibaseseq[A*B] with A = + .5'i + .5'j + .5'k + .5e and B = - .5'i - .25'j + .25'k - .5i' - .25j' + .25k' - .5'ii' - .25'ij' - .25'ik' - .25'ji' - .25'ki' - .5e

PARI

Vec((1 - x + 2*x^2) / (1 - x^3 + x^4) + O(x^55)) \\ Colin Barker, May 11 2019

Formula

a(n) = a(n-3) - a(n-4) for n>3. - Colin Barker, May 11 2019