A011761 - OEIS

A011761

a(n) = a(n-1) + a(n-3), with a(0) = a(1) = 1, a(2) = 5.

1, 1, 5, 6, 7, 12, 18, 25, 37, 55, 80, 117, 172, 252, 369, 541, 793, 1162, 1703, 2496, 3658, 5361, 7857, 11515, 16876, 24733, 36248, 53124, 77857, 114105, 167229, 245086, 359191, 526420, 771506, 1130697

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (1,0,1).

FORMULA

G.f.: (1+4*x^2)/(1-x-x^3). - G. C. Greubel, May 01 2017 [Corrected by Georg Fischer, May 18 2019]

MATHEMATICA

a[0] := 1; a[1] := 1; a[2] = 5; a[n_] := a[n] =a[n - 1] + a[n - 3]; Table[a[n], {n, 50}] (* Alonso del Arte, Dec 05 2011 *)

LinearRecurrence[{1, 0, 1}, {1, 1, 5}, 40] (* Harvey P. Dale, Aug 09 2012 *)

CoefficientList[Series[(1 + 4*x^2)/(1 - x - x^3), {x, 0, 50}], x] (* G. C. Greubel, May 01 2017 *)

PROG

(PARI) x='x+O('x^50); Vec((1+4*x^2)/(1-x-x^3)) \\ G. C. Greubel, May 01 2017; corrected by Georg Fischer, May 18 2019

CROSSREFS

Cf. A000930.

Sequence in context: A047320 A327301 A247522 * A106745 A165776 A327106

Adjacent sequences: A011758 A011759 A011760 * A011762 A011763 A011764

KEYWORD

nonn

AUTHOR

Juan-Carlos Lerman (jclerm(AT)aztec.asu.edu)

EXTENSIONS

Name corrected by Arkadiusz Wesolowski, Dec 05 2011

STATUS

approved