A110064 a(n+4) = a(n+1) - a(n), a(0) = 1, a(1) = -4, a(2) = 0, a(3) = 1.

1, -4, 0, 1, -5, 4, 1, -6, 9, -3, -7, 15, -12, -4, 22, -27, 8, 26, -49, 35, 18, -75, 84, -17, -93, 159, -101, -76, 252, -260, 25, 328, -512, 285, 303, -840, 797, 18, -1143, 1637, -779, -1161, 2780, -2416, -382, 3941, -5196, 2034, 4323, -9137, 7230, 2289, -13460, 16367, -4941, -15749, 29827, -21308, -10808

Offset: 0

Author

Creighton Dement, Jul 10 2005

Keywords

• easy
• sign

Comments

One of several sequences, apparently all of the form a(n+4) = a(n+1) - a(n), which appear to "spiral outwards" when plotted against each other (see A110061-64). In reference to the FAMP program code, A017817 is also in this same batch of sequences and satisfies the same recurrence relation.

Links

• Index entries for linear recurrences with constant coefficients, signature (0,0,1,-1).

Crossrefs

Cf. A110061, A110062, A110063, A017817.

Programs

Maple

seriestolist(series(-(-1+4*x)/(1-x^3+x^4), x=0,60)); -or- Floretion Algebra Multiplication Program, FAMP Code: 4kbaseseq[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

LinearRecurrence[{0,0,1,-1},{1,-4,0,1},60] (* Harvey P. Dale, Oct 23 2016 *)

Formula

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