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A214831 a(n) = a(n-1) + a(n-2) + a(n-3), with a(0) = 1, a(1) = a(2) = 9. 13
1, 9, 9, 19, 37, 65, 121, 223, 409, 753, 1385, 2547, 4685, 8617, 15849, 29151, 53617, 98617, 181385, 333619, 613621, 1128625, 2075865, 3818111, 7022601, 12916577, 23757289, 43696467, 80370333, 147824089, 271890889, 500085311, 919800289, 1691776489 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Part of a group of sequences defined by a(0), a(1)=a(2), a(n)=a(n-1)+a(n-2)+a(n-3) which is a sub-group of sequences with linear recurrences and constant coefficients listed in the index. See comments in A214727.

LINKS

Robert Price, Table of n, a(n) for n = 0..1000

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

FORMULA

G.f.: (1+8*x-x^2)/(1-x-x^2-x^3).

a(n) = -A000073(n) + 8*A000073(n+1) + A000073(n+2). - G. C. Greubel, Apr 24 2019

MATHEMATICA

LinearRecurrence[{1, 1, 1}, {1, 9, 9}, 40] (* Harvey P. Dale, Oct 11 2017 *)

PROG

(PARI) Vec((x^2-8*x-1)/(x^3+x^2+x-1) + O(x^40)) \\ Michel Marcus, Jul 08 2014

(MAGMA) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1+8*x-x^2)/(1-x-x^2-x^3) )); // G. C. Greubel, Apr 24 2019

(Sage) ((1+8*x-x^2)/(1-x-x^2-x^3)).series(x, 40).coefficients(x, sparse=False) # G. C. Greubel, Apr 24 2019

(GAP) a:=[1, 9, 9];; for n in [4..40] do a[n]:=a[n-1]+a[n-2]+a[n-3]; od; a; # G. C. Greubel, Apr 24 2019

CROSSREFS

Cf. A000213, A000288, A000322, A000383, A060455, A136175, A141036, A141523, A214825-A214831, A244930, A244931.

Sequence in context: A022092 A245430 A161365 * A197497 A053456 A144424

Adjacent sequences:  A214828 A214829 A214830 * A214832 A214833 A214834

KEYWORD

nonn,easy

AUTHOR

Abel Amene, Aug 07 2012

STATUS

approved

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Last modified February 23 06:00 EST 2020. Contains 332159 sequences. (Running on oeis4.)