A012814 Take every 5th term of Padovan sequence A000931, beginning with the third term.

0, 1, 5, 21, 86, 351, 1432, 5842, 23833, 97229, 396655, 1618192, 6601569, 26931732, 109870576, 448227521, 1828587033, 7459895657, 30433357674, 124155792775, 506505428836, 2066337330754, 8429820731201

Offset

0,3

Links

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

Ulrich Brenner, Anna Hermann, and Jannik Silvanus, Constructing Depth-Optimum Circuits for Adders and AND-OR Paths, arXiv:2012.05550 [cs.DM], 2020.

Index entries for linear recurrences with constant coefficients, signature (5,-4,1).

Formula

a(n+3) = 5*a(n+2) - 4*a(n+1) + a(n).

G.f.: x/(1-5*x+4*x^2-x^3). - Colin Barker, Feb 03 2012

a(n) = A012855(n+4) - A012855(n+3).

Example

G.f. = x + 5*x^2 + 21*x^3 + 86*x^4 + 351*x^5 + 1432*x^6 + 5842*x^7 + ...

Mathematica

LinearRecurrence[{5, -4, 1}, {0, 1, 5}, 25] (* Vincenzo Librandi, Feb 03 2012 *)

Prog

(Magma) I:=[0, 1, 5 ]; [n le 3 select I[n] else 5*Self(n-1)-4*Self(n-2)+Self(n-3): n in [1..40]]; // Vincenzo Librandi, Feb 03 2012

Crossrefs

Cf. A000931, A012855.

Sequence in context: A097113 A368345 A265939 * A039919 A322875 A292494

Adjacent sequences: A012811 A012812 A012813 * A012815 A012816 A012817

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

Initial term 0 added by Colin Barker, Feb 03 2012

Status

approved