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A226311 a(n+5) = a(n+4)+a(n+3)+a(n+2)+a(n+1)+2*a(n) with a(0)=2, a(1)=1, a(2)=5, a(3)=10, a(4)=20. 1
2, 1, 5, 10, 20, 40, 77, 157, 314, 628, 1256, 2509, 5021, 10042, 20084, 40168, 80333, 160669, 321338, 642676, 1285352, 2570701, 5141405, 10282810, 20565620, 41131240, 82262477, 164524957, 329049914, 658099828, 1316199656, 2632399309, 5264798621, 10529597242, 21059194484, 42118388968, 84236777933, 168473555869 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Charles K. Cook and Michael R. Bacon, Some identities for Jacobsthal and Jacobsthal-Lucas numbers satisfying higher order recurrence relations, Annales Mathematicae et Informaticae, 41 (2013) pp. 27-39.

YĆ¼ksel Soykan, Sum Formulas for Generalized Fifth-Order Linear Recurrence Sequences, Journal of Advances in Mathematics and Computer Science (2019) Vol. 34, No. 5, 1-14.

Index entries for linear recurrences with constant coefficients, signature (1,1,1,1,2).

FORMULA

G.f.: -(2*x^4+2*x^3+2*x^2-x+2) / ((2*x-1)*(x^4+x^3+x^2+x+1)). - Colin Barker, Jun 08 2013

MAPLE

f:=proc(n) option remember;

if n=0 then 2 elif n=1 then 1 elif n=2 then 5 elif n=3 then 10 elif n=4 then 20 else

f(n-1)+f(n-2)+f(n-3)+f(n-4)+2*f(n-5); fi; end;

[seq(f(n), n=0..40)];

MATHEMATICA

CoefficientList[Series[-(2 x^4 + 2 x^3 + 2 x^2 - x + 2) / ((2 x - 1) (x^4 + x^3 + x^2 + x + 1)), {x, 0, 40}], x] (* Vincenzo Librandi, Jun 19 2013 *)

LinearRecurrence[{1, 1, 1, 1, 2}, {2, 1, 5, 10, 20}, 20] (* Harvey P. Dale, Jan 20 2015 *)

CROSSREFS

Sequence in context: A174218 A226308 A226309 * A049948 A222574 A222680

Adjacent sequences:  A226308 A226309 A226310 * A226312 A226313 A226314

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Jun 08 2013

STATUS

approved

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Last modified July 15 02:31 EDT 2020. Contains 335762 sequences. (Running on oeis4.)