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A110528 a(n+3) = 3*a(n+2) + 5*a(n+1) + a(n), a(0) = 1, a(1) = 10, a(2) = 37. 3
1, 10, 37, 162, 681, 2890, 12237, 51842, 219601, 930250, 3940597, 16692642, 70711161, 299537290, 1268860317, 5374978562, 22768774561, 96450076810, 408569081797, 1730726404002, 7331474697801, 31056625195210 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

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).

FORMULA

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

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

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

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 *)

PROG

(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

CROSSREFS

Cf. A110526, A110527.

Sequence in context: A048480 A116970 A199208 * A208674 A137280 A071261

Adjacent sequences:  A110525 A110526 A110527 * A110529 A110530 A110531

KEYWORD

easy,nonn,changed

AUTHOR

Creighton Dement, Jul 24 2005

STATUS

approved

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Last modified November 21 16:27 EST 2017. Contains 295003 sequences.