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

Offset: 0

Author

Creighton Dement, Aug 09 2005

Keywords

• easy
• sign

Comments

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

Links

• Robert Munafo, Sequences Related to Floretions
• Index entries for linear recurrences with constant coefficients, signature (0, -4, 0, -1).

Crossrefs

Cf. A054491, A001353, A002530.

Programs

Maple

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

Mathematica

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

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)