login
A113976
a(n) = 4*a(n-1) - 3*a(n-2), for n>3, with a(0) = 14, a(1) = 133, a(2) = 616, and a(3) = 2128.
1
14, 133, 616, 2128, 6664, 20272, 61096, 183568, 550984, 1653232, 4959976, 14880208, 44640904, 133922992, 401769256, 1205308048, 3615924424, 10847773552, 32543320936, 97629963088, 292889889544, 878669668912
OFFSET
0,1
FORMULA
G.f.: 7*(1+x)*(1+3*x)*(2+3*x)/((1-x)*(1-3*x)).
a(n) = 28*(3^(n+1) - 5), n>1.
E.g.f.: 7*(10 + 3*x - 20*exp(x) + 12*exp(3*x)). - G. C. Greubel, Jul 07 2021
MATHEMATICA
CoefficientList[Series[7*(1+x)*(1+3*x)*(2+3*x)/((1-x)*(1-3*x)), {x, 0, 40}], x] (* modified by G. C. Greubel, Jul 07 2021 *)
Join[{14, 133}, LinearRecurrence[{4, -3}, {616, 2128}, 20]] (* Harvey P. Dale, Nov 14 2011 *)
PROG
(Magma) [14, 133] cat [28*(3^(n+1) - 5): n in [2..40]]; // G. C. Greubel, Jul 07 2021
(Sage) [14, 133]+[28*(3^(n+1) - 5) for n in (2..40)] # G. C. Greubel, Jul 07 2021
(PARI) a(n)=if(n>1, ([0, 1; -3, 4]^n*[-56; 112])[1, 1], 119*n+14) \\ Charles R Greathouse IV, Jul 08 2024
CROSSREFS
Cf. A113923.
Sequence in context: A021114 A328785 A375894 * A022738 A017269 A021079
KEYWORD
nonn,easy
AUTHOR
Roger L. Bagula, Jan 31 2006
EXTENSIONS
Definition replaced by recurrence by the Associate Editors of the OEIS, Sep 28 2009
Edited by G. C. Greubel, Jul 07 2021
STATUS
approved