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A214825 a(n) = a(n-1) + a(n-2) + a(n-3), with a(0) = 1, a(1) = a(2) = 3. 49
1, 3, 3, 7, 13, 23, 43, 79, 145, 267, 491, 903, 1661, 3055, 5619, 10335, 19009, 34963, 64307, 118279, 217549, 400135, 735963, 1353647, 2489745, 4579355, 8422747, 15491847, 28493949, 52408543, 96394339, 177296831, 326099713, 599790883, 1103187427 (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

Indranil Ghosh, Table of n, a(n) for n = 0..3770

Martin Burtscher, Igor Szczyrba, RafaƂ Szczyrba, Analytic Representations of the n-anacci Constants and Generalizations Thereof, Journal of Integer Sequences, Vol. 18 (2015), Article 15.4.5.

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

FORMULA

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

MATHEMATICA

LinearRecurrence[{1, 1, 1}, {1, 3, 3}, 40] (* Harvey P. Dale, Oct 05 2013 *)

PROG

(PARI) a(n)=([0, 1, 0; 0, 0, 1; 1, 1, 1]^n*[1; 3; 3])[1, 1] \\ Charles R Greathouse IV, Mar 22 2016

CROSSREFS

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

Sequence in context: A065876 A204858 A095008 * A230017 A134346 A049772

Adjacent sequences:  A214822 A214823 A214824 * A214826 A214827 A214828

KEYWORD

nonn,easy

AUTHOR

Abel Amene, Jul 28 2012

STATUS

approved

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Last modified February 25 18:12 EST 2018. Contains 299655 sequences. (Running on oeis4.)