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

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (5, -4, 1).

Crossrefs

Cf. A012781 (partial sums).

Programs

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

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 *)

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