A012772 Take every 5th term of Padovan sequence A000931, beginning with the sixth term.

1, 3, 12, 49, 200, 816, 3329, 13581, 55405, 226030, 922111, 3761840, 15346786, 62608681, 255418101, 1042002567, 4250949112, 17342153393, 70748973084, 288627200960, 1177482265857, 4803651498529, 19596955630177

Offset

0,2

Links

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

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.: (1-x)^2/(1-5*x+4*x^2-x^3). - Colin Barker, Feb 02 2012

Mathematica

CoefficientList[Series[(1-x)^2/(1-5*x+4*x^2-x^3), {x, 0, 33}], x] (* Vincenzo Librandi, Apr 18 2012 *)
LinearRecurrence[{5, -4, 1}, {1, 3, 12}, 30] (* Harvey P. Dale, Aug 15 2024 *)

Prog

(Magma) I:=[1, 3, 12]; [n le 3 select I[n] else 5*Self(n-1)-4*Self(n-2)+Self(n-3): n in [1..30]]; // Vincenzo Librandi, Apr 18 2012

Crossrefs

Cf. A012781 (partial sums).

Sequence in context: A248347 A037758 A037646 * A012864 A045890 A049673

Adjacent sequences: A012769 A012770 A012771 * A012773 A012774 A012775

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved