A110210 a(n+3) = 6*a(n) - 5*a(n+2), a(0) = -1, a(1) = 1, a(2) = -5.

-1, 1, -5, 19, -89, 415, -1961, 9271, -43865, 207559, -982169, 4647655, -21992921, 104071591, -492472025, 2330402599, -11027583449, 52183085095, -246933009881, 1168499548711, -5529399232985, 26165398105639, -123815993235929, 585903570781735, -2772525465274841

Offset

0,3

Links

Table of n, a(n) for n=0..24.

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

Formula

Superseeker finds: a(n+1) - a(n) = ((-1)^n)*A094433(n+2) (left term in M^n * [1 0 0], M = the 3 X 3 matrix [1 -1 0 / -1 3 -2 / 0 -2 2], offset at 1); a(n+2) - a(n) = ((-1)^(n+1))*A086405(n+1) (Row T(n, 3) of number array A086404.

g.f.: (4*x+1)/(6*x^3-5*x-1). - Harvey P. Dale, Nov 09 2014

Maple

seriestolist(series((1+4*x)/((x-1)*(6*x^2+6*x+1)), x=0, 25)); -or- Floretion Algebra Multiplication Program, FAMP Code: 2baseisumseq[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)

Mathematica

LinearRecurrence[{-5, 0, 6}, {-1, 1, -5}, 30] (* or *) CoefficientList[ Series[ (1+4*x)/(-1-5*x+6*x^3), {x, 0, 30}], x] (* Harvey P. Dale, Nov 09 2014 *)

Crossrefs

Cf. A094433, A110211, A110212, A110213.

Sequence in context: A301702 A296162 A144036 * A244899 A147139 A330445

Adjacent sequences: A110207 A110208 A110209 * A110211 A110212 A110213

Keyword

easy,sign

Author

Creighton Dement, Jul 16 2005

Status

approved