A137213 First differences of A137212.

0, 1, 4, 15, 52, 173, 560, 1779, 5576, 17305, 53308, 163287, 497980, 1513541, 4587944, 13878075, 41910032, 126395953, 380795380, 1146267039, 3448170436, 10367130845, 31156000928, 93599839107, 281117798360, 844121793481

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 (5,-5,-3).

Formula

From R. J. Mathar, Mar 17 2008: (Start)

O.g.f.: 1/(1-3*x) - 1/(1-2*x-x^2) = x*(1-x)/( (1-3*x)*(1-2*x-x^2) ).

a(n) = 3^n - A000129(n+1). (End)

Mathematica

LinearRecurrence[{5, -5, -3}, {0, 1, 4}, 30] (* Harvey P. Dale, Apr 18 2019 *)

Prog

(Magma) [n le 3 select (n-1)^2 else 5*Self(n-1) -5*Self(n-2) -3*Self(n-3): n in [1..31]]; // G. C. Greubel, Jan 05 2022
(Sage) [3^n - lucas_number1(n+1, 2, -1) for n in (0..30)] # G. C. Greubel, Jan 05 2022

Crossrefs

Cf. A000129, A132894, A137212.

Sequence in context: A003013 A117202 A291011 * A027853 A132894 A117917

Adjacent sequences: A137210 A137211 A137212 * A137214 A137215 A137216

Keyword

nonn

Author

Paul Curtz, Mar 06 2008

Extensions

More terms from R. J. Mathar, Mar 17 2008

Status

approved