A111352 a(n+3) = a(n+2) + 3*a(n+1) + a(n).

1, -1, 2, 0, 5, 7, 22, 48, 121, 287, 698, 1680, 4061, 9799, 23662, 57120, 137905, 332927, 803762, 1940448, 4684661, 11309767, 27304198, 65918160, 159140521, 384199199, 927538922, 2239277040, 5406093005

Offset

0,3

Comments

a(n) + a(n+1) = A000129(n); a(n+2) - a(n) = A001333(n)

Floretion Algebra Multiplication Program, FAMP Code: 2jbasekrokseq[A*H] with A = + .25'i + .25i' + .25'ii' + .25'jj' + .25'kk' + .25'jk' + .25'kj' + .25e; H = - 2'i - 'j + 'k; roktype : Y[15] = Y[15] + (-1)^p (internal program code)

Links

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Robert Munafo, Sequences Related to "Floretions".

Index entries for linear recurrences with constant coefficients, signature (1,3,1).

Formula

a(n) = (1/4*sqrt(2)-1/4)*(1+sqrt(2))^n + (-1/4*sqrt(2)-1/4)*(1-sqrt(2))^n + 3/2*(-1)^n.

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

a(n) = 3*(-1)^n/2+A001333(n-1)/2, n>0. [R. J. Mathar, Nov 10 2009]

Mathematica

LinearRecurrence[{1, 3, 1}, {1, -1, 2}, 30] (* Harvey P. Dale, Jul 26 2020 *)

Crossrefs

Cf. A000129, A001333.

Sequence in context: A084258 A171016 A321205 * A173343 A334059 A133446

Adjacent sequences: A111349 A111350 A111351 * A111353 A111354 A111355

Keyword

easy,sign

Author

Creighton Dement, Oct 29 2005

Status

approved