A110211 a(n+3) = 6*a(n) - 5*a(n+2), a(0) = -1, a(1) = 3, a(2) = -15.

-1, 3, -15, 69, -327, 1545, -7311, 34593, -163695, 774609, -3665487, 17345265, -82078671, 388400433, -1837930575, 8697180849, -41155501647, 194749924785, -921566538831, 4360899684273, -20635998872655, 97650595130289, -462087577545807, 2186621894493105

Offset

0,2

Comments

Floretion Algebra Multiplication Program, FAMP Code: 1kbasesumseq[A*B] with A = + 'i + 'ii' + 'ij' + 'ik' and B = + .5'i - .5'j + .5'k + .5i' + .5j' - .5k' - .5'ij' - .5'ik' + .5'ji' + .5'ki' Sumtype is set to: sum[(Y[0], Y[1], Y[2]),mod(3).

Links

Table of n, a(n) for n=0..23.

Index entries for linear recurrences with constant coefficients, signature (-5,0,6).

Formula

G.f.: (1+2*x)/((x-1)*(6*x^2+6*x+1)).

a(n) = (-3+(-3-sqrt(3))^n*(-5-2*sqrt(3))+(-3+sqrt(3))^n*(-5+2*sqrt(3)))/13. - Harvey P. Dale, Mar 28 2012 [corrected by Jason Yuen, Aug 29 2025]

Maple

S := taylor((1+2*x)/((x-1)*(6*x^2+6*x+1)), x, 25):
seq(coeff(S, x, n), n=0..20);

Mathematica

LinearRecurrence[{-5, 0, 6}, {-1, 3, -15}, 30] (* Harvey P. Dale, Mar 28 2012 *)

Crossrefs

Cf. A110210, A110212, A110213.

Sequence in context: A213451 A224749 A122558 * A167874 A318967 A277370

Adjacent sequences: A110208 A110209 A110210 * A110212 A110213 A110214

Keyword

easy,sign

Author

Creighton Dement, Jul 16 2005

Status

approved