OFFSET
0,4
COMMENTS
Starting at 1, the three-fold convolution of A001020 (powers of 11).
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..400
Index entries for linear recurrences with constant coefficients, signature (33,-363,1331).
FORMULA
a(n) = 33*a(n-1) - 363*a(n-2) + 1331*a(n-3), a(0) = a(1) = 0, a(2) = 1.
a(n) = 11^(n-2)*binomial(n, 2).
G.f.: x^2/(1 - 11*x)^3.
E.g.f.: (1/2)*exp(11*x)*x^2. - Franck Maminirina Ramaharo, Nov 23 2018
From Amiram Eldar, Jan 06 2022: (Start)
Sum_{n>=2} 1/a(n) = 22 - 220*log(11/10).
Sum_{n>=2} (-1)^n/a(n) = 264*log(12/11) - 22. (End)
MAPLE
seq((11)^(n-2)*binomial(n, 2), n=0..30); # G. C. Greubel, May 13 2021
MATHEMATICA
LinearRecurrence[{33, -363, 1331}, {0, 0, 1}, 30] (* Harvey P. Dale, Dec 15 2014 *)
PROG
(Magma) [11^(n-2)*Binomial(n, 2): n in [0..20]]; // Vincenzo Librandi, Oct 16 2011
(PARI) vector(20, n, n--; 11^(n-2)*binomial(n, 2)) \\ G. C. Greubel, Nov 23 2018
(Sage) [11^(n-2)*binomial(n, 2) for n in range(20)] # G. C. Greubel, Nov 23 2018
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Mar 08 2003
STATUS
approved