A109731 - OEIS

A109731

a(n) = - 4*a(n-2) - a(n-4), a(0) = 1, a(1) = -4, a(2) = -6, a(3) = 15.

1, -4, -6, 15, 23, -56, -86, 209, 321, -780, -1198, 2911, 4471, -10864, -16686, 40545, 62273, -151316, -232406, 564719, 867351, -2107560, -3236998, 7865521, 12080641, -29354524, -45085566, 109552575, 168261623, -408855776

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OFFSET

0,2

COMMENTS

Sequence A002530 and A002531 are also generated by the floretion given in the program code.

Floretion Algebra Multiplication Program, FAMP Code: 1lestesseq[A*B] with A = + .25'i + .25i' + 'ij' + .25'jk' + .25'kj' and B = + j' + k' + 'ii'.

LINKS

Table of n, a(n) for n=0..29.

Robert Munafo, Sequences Related to Floretions.

Index entries for linear recurrences with constant coefficients, signature (0,-4,0,-1).

FORMULA

a(2n) = ((-1)^n)*A054491(n), a(2n+1) = ((-1)^n+1)*A001353(n+1). G.f. (1-4*x-2*x^2-x^3)/(x^4+4*x^2+1)

MATHEMATICA

LinearRecurrence[{0, -4, 0, -1}, {1, -4, -6, 15}, 40] (* Harvey P. Dale, Mar 05 2013 *)

CROSSREFS

Cf. A054491, A001353, A002530.

Sequence in context: A346297 A034765 A300276 * A369437 A027631 A128620

Adjacent sequences: A109728 A109729 A109730 * A109732 A109733 A109734

KEYWORD

easy,sign

AUTHOR

Creighton Dement, Aug 09 2005

STATUS

approved