OFFSET
0,4
COMMENTS
Starting at 1, the three-fold convolution of A001018 (powers of 8).
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..400
Index entries for linear recurrences with constant coefficients, signature (24,-192,512).
FORMULA
a(n) = 24*a(n-1) - 192*a(n-2) + 512*a(n-3) for n>2, a(0)=a(1)=0, a(2)=1.
a(n) = 8^(n-2)*binomial(n, 2).
G.f.: x^2/(1 - 8*x)^3.
E.g.f.: (x^2/2)*exp(8*x). - G. C. Greubel, May 13 2021
From Amiram Eldar, Jan 06 2022: (Start)
Sum_{n>=2} 1/a(n) = 16 - 112*log(8/7).
Sum_{n>=2} (-1)^n/a(n) = 144*log(9/8) - 16. (End)
MATHEMATICA
LinearRecurrence[{24, -192, 512}, {0, 0, 1}, 30] (* Harvey P. Dale, Jun 08 2014 *)
PROG
(Magma) [8^n*Binomial(n+2, 2): n in [-2..20]]; // Vincenzo Librandi, Oct 16 2011
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Mar 08 2003
STATUS
approved