OFFSET
0,3
LINKS
Harry J. Smith, Table of n, a(n) for n = 0..200
Index entries for linear recurrences with constant coefficients, signature (6,-12,10,-3).
FORMULA
From G. C. Greubel, Jun 13 2022: (Start)
a(n) = 3^n - binomial(n+2, 2).
G.f.: x^2*(3-x)/((1-x)^3 * (1-3*x)).
E.g.f.: exp(3*x) - (1/2)*(2 + 4*x + x^2)*exp(x). (End)
MATHEMATICA
LinearRecurrence[{6, -12, 10, -3}, {0, 0, 3, 17}, 40] (* G. C. Greubel, Jun 13 2022 *)
PROG
(PARI) { for (n=0, 200, write("b061982.txt", n, " ", 3^n - (n + 1)*(n + 2)/2) ) } \\ Harry J. Smith, Jul 29 2009
(Magma) [3^n -Binomial(n+2, 2): n in [0..40]]; // G. C. Greubel, Jun 13 2022
(SageMath) [3^n -binomial(n+2, 2) for n in (0..40)] # G. C. Greubel, Jun 13 2022
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Henry Bottomley, May 24 2001
STATUS
approved