A110061 Expansion of x^2*(-3+4*x)/(1-x^3+x^4).

0, 0, -3, 4, 0, -3, 7, -4, -3, 10, -11, 1, 13, -21, 12, 12, -34, 33, 0, -46, 67, -33, -46, 113, -100, -13, 159, -213, 87, 172, -372, 300, 85, -544, 672, -215, -629, 1216, -887, -414, 1845, -2103, 473, 2259, -3948, 2576, 1786, -6207, 6524, -790, -7993, 12731, -7314, -7203, 20724, -20045, 111, 27927, -40769, 20156

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 A110062-64).

Links

• Robert Munafo, Sequences Related to Floretions
• Index entries for linear recurrences with constant coefficients, signature (0,0,1,-1).

Crossrefs

Cf. A110062, A110063, A110064.

Programs

Maple

seriestolist(series(x^2*(-3+4*x)/(1-x^3+x^4), x=0,30)); -or- 4tesseq[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

Mathematica

CoefficientList[Series[x^2(-3+4x)/(1-x^3+x^4),{x,0,100}],x] (* or *) LinearRecurrence[{0,0,1,-1},{0,0,-3,4},100] (* Harvey P. Dale, Nov 04 2021 *)