OFFSET
0,2
COMMENTS
a(n) is the number of full-dimensional lattices in Z^(n+1) with volume 10. - Álvar Ibeas, Nov 29 2015
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (18,-97,180,-100).
FORMULA
a(n) = 1/4*(2^(n+1)-1)*(5^(n+1)-1). E.g., a(1) = 1/4*(2^2-1)*(5^2-1) = 18. - Vladeta Jovovic, Dec 18 2001
a(n) = 18*a(n-1)-97*a(n-2)+180*a(n-3)-100*a(n-4). - Colin Barker, Jan 27 2015
G.f.: -(10*x^2-1) / ((x-1)*(2*x-1)*(5*x-1)*(10*x-1)). - Colin Barker, Jan 27 2015
EXAMPLE
At 10^1 the factors are 1, 2, 5, 10. The sum of these factors is 18: 1 + 2 + 5 + 10.
MATHEMATICA
Table[DivisorSigma[1, 10^n], {n, 0, 18}] (* Jayanta Basu, Jun 30 2013 *)
PROG
(Magma) [1/4*(2^(n+1)-1)*(5^(n+1)-1): n in [0..20]]; // Vincenzo Librandi, Oct 03 2011
(PARI) Vec(-(10*x^2-1)/((x-1)*(2*x-1)*(5*x-1)*(10*x-1)) + O(x^100)) \\ Colin Barker, Jan 27 2015
(PARI) a(n) = sigma(10^n); \\ Altug Alkan, Dec 04 2015
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
STATUS
approved