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

Author

Paul Curtz, Mar 06 2008

Keywords

• nonn

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).

Crossrefs

Cf. A000129, A132894, A137212.

Programs

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

Mathematica

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

Sage

[3^n - lucas_number1(n+1,2,-1) for n in (0..30)] # G. C. Greubel, Jan 05 2022

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)

Extensions

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