OFFSET
1,2
COMMENTS
Binomial transform of 1,24,12,0,0,0,....
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
a(n) = 6*n^2 + 6*n - 11.
a(n) = 2*a(n-1) - a(n-2) + 12.
G.f.: x*(1 + 22*x - 11*x^2)/(1-x)^3.
a(n) - a(n-1) = A008594(n) for n > 1.
From G. C. Greubel, May 27 2016: (Start)
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
E.g.f.: (-11 + 12*x + 6*x^2)*exp(x) + 11. (End)
MATHEMATICA
LinearRecurrence[{3, -3, 1}, {1, 25, 61}, 50] (* G. C. Greubel, May 27 2016 *)
PROG
(Magma) [ n eq 1 select 1 else Self(n-1)+12*n: n in [1..44] ];
(PARI) a(n)=6*n^2+6*n-11 \\ Charles R Greathouse IV, Jun 17 2017
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Klaus Brockhaus, Oct 22 2009
STATUS
approved