login
A137213
First differences of A137212.
1
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
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
KEYWORD
nonn
AUTHOR
Paul Curtz, Mar 06 2008
EXTENSIONS
More terms from R. J. Mathar, Mar 17 2008
STATUS
approved