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A110527 a(n+3) = 3*a(n+2) + 5*a(n+1) + a(n), a(0) = 0, a(1) = 1, a(2) = 8. 3
0, 1, 8, 29, 128, 537, 2280, 9653, 40896, 173233, 733832, 3108557, 13168064, 55780809, 236291304, 1000946021, 4240075392, 17961247585, 76085065736, 322301510525, 1365291107840, 5783465941881, 24499154875368 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

A048878(n) = a(n) + a(n+1). Compare with A110526.

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (3,5,1).

FORMULA

G.f.: -x*(1+5*x)/((1+x)*(x^2+4*x-1)).

a(n) = -(1/2)*(2 - sqrt(5))^n + (-1)^n - (1/2)*(2 + sqrt(5))^n + (2/5)*(2 + sqrt(5))^n*sqrt(5) - (2/5)*(2 - sqrt(5))^n*sqrt(5), with n >= 0. - Paolo P. Lava, Oct 02 2008

a(n) = (-1)^n + 3*Fibonacci(3*n)/2 - Fibonacci(3*n - 1). - Ehren Metcalfe, Nov 18 2017

MAPLE

seriestolist(series(-x*(1+5*x)/((1+x)*(x^2+4*x-1)), x=0, 25)); -or- Floretion Algebra Multiplication Program, FAMP Code: 1lesseq[(- 'i + 'j - i' + j' - 'kk' - 'ik' - 'jk' - 'ki' - 'kj')(+ .5'i + .5i' + .5'jj' + .5'kk')], apart from initial term.

MATHEMATICA

LinearRecurrence[{3, 5, 1}, {0, 1, 8}, 30] (* Harvey P. Dale, Feb 12 2015 *)

PROG

(PARI) x='x+O('x^50); concat(0, Vec(-x*(1+5*x)/((1+x)*(x^2+4*x-1)))) \\ G. C. Greubel, Aug 30 2017

CROSSREFS

Cf. A110526, A110528, A033887, A001076, A049661, A033887.

Sequence in context: A199207 A088131 A072264 * A189946 A239855 A239029

Adjacent sequences:  A110524 A110525 A110526 * A110528 A110529 A110530

KEYWORD

easy,nonn,changed

AUTHOR

Creighton Dement, Jul 24 2005

STATUS

approved

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Last modified November 21 07:06 EST 2017. Contains 294992 sequences.