A173343 -id:A173343 - cp's OEIS frontend

A173344 a(n+4) = a(n+3) - 2*a(n+2) - a(n+1) - a(n), starting with (0, 1, 0, -2).

0, 1, 0, -2, -3, 0, 8, 13, 0, -34, -55, 0, 144, 233, 0, -610, -987, 0, 2584, 4181, 0, -10946, -17711, 0, 46368, 75025, 0, -196418, -317811, 0, 832040, 1346269, 0, -3524578, -5702887, 0, 14930352, 24157817, 0, -63245986, -102334155, 0

Offset: 0

Creighton Dement, Feb 16 2010

See A173343. A151889 gives a nonnegative version without zeros. (a(n)) = kibseq(X) with X = -0.25'i + 0.5'j + 0.5'k + 0.25'i + j' + 0.5k' - 0.25ii - 0.25'jj' - 0.25'kk' + 0.5'ij' + 0.5'ik' - 0.5'ji' -0.25'jk' + 0.25'kj' + 0.25'ee' (see Munafo link for definitions).

C. Dement, Online Floretion Multiplier [broken link]
R. Munafo, Sequences Related to Floretions
Index entries for linear recurrences with constant coefficients, signature (1,-2,-1,-1).

Cf. A151889, A173343, A275858.

CoefficientList[Series[(x-x^2)/(1-x+2 x^2+x^3+x^4),{x,0,50}],x]  (* Harvey P. Dale, Apr 01 2011 *)

concat(0, Vec((x-x^2)/(x^4+x^3+2*x^2-x+1) + O(x^50))) \\ Michel Marcus, Oct 29 2022

G.f.: x*(1-x)/(x^4+x^3+2*x^2-x+1).

a(n) = A275858(n-1)-A275858(n-2). - R. J. Mathar, Mar 23 2023

Name edited by Michel Marcus, Oct 29 2022

cp's OEIS Frontend

A173344 a(n+4) = a(n+3) - 2*a(n+2) - a(n+1) - a(n), starting with (0, 1, 0, -2).

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