A110528 a(n+3) = 3*a(n+2) + 5*a(n+1) + a(n), a(0) = 1, a(1) = 10, a(2) = 37.

1, 10, 37, 162, 681, 2890, 12237, 51842, 219601, 930250, 3940597, 16692642, 70711161, 299537290, 1268860317, 5374978562, 22768774561, 96450076810, 408569081797, 1730726404002, 7331474697801, 31056625195210

Offset: 0

Author

Creighton Dement, Jul 24 2005

Keywords

• easy
• nonn

Comments

Compare with A110526, A110527.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Robert Munafo, Sequences Related to Floretions
• Index entries for linear recurrences with constant coefficients, signature (3,5,1).

Crossrefs

Cf. A110526, A110527.

Programs

Maple

seriestolist(series(-(1+7*x+2*x^2)/((1+x)*(x^2+4*x-1)), x=0,25)); -or- Floretion Algebra Multiplication Program, FAMP Code: 2tesseq[(- 'i + 'j - i' + j' - 'kk' - 'ik' - 'jk' - 'ki' - 'kj')(+ .5'i + .5i' + .5'jj' + .5'kk')]

Mathematica

LinearRecurrence[{3,5,1},{1,10,37},30] (* Harvey P. Dale, Apr 21 2016 *)

PARI

x='x+O('x^50); Vec(-(1+7*x+2*x^2)/((1+x)*(x^2+4*x-1))) \\ G. C. Greubel, Aug 30 2017

Formula

G.f.: -(1 + 7*x + 2*x^2)/((1 + x)*(x^2 + 4*x - 1)).

a(n) = A001077(n+1) - (-1)^n. - Ehren Metcalfe, Nov 18 2017