A110527 a(n+3) = 3*a(n+2) + 5*a(n+1) + a(n), a(0) = 0, a(1) = 1, a(2) = 8.

0, 1, 8, 29, 128, 537, 2280, 9653, 40896, 173233, 733832, 3108557, 13168064, 55780809, 236291304, 1000946021, 4240075392, 17961247585, 76085065736, 322301510525, 1365291107840, 5783465941881, 24499154875368

Offset: 0

Author

Creighton Dement, Jul 24 2005

Keywords

• easy
• nonn

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).

Crossrefs

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

Programs

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 *)

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

Formula

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

a(n) = (-1)^n + 3*A001076(n) - A015448(n). - Ehren Metcalfe, Nov 18 2017

a(n) = (-1)^n + 2*A110526(n) + A110679(n-2) for n >= 2. - Yomna Bakr and Greg Dresden, May 25 2024