OFFSET
0,3
COMMENTS
More generally, the ordinary generating function for the squares of k-gonal numbers is x*(1 + (k^2 - 5)*x + (4*k^2 - 18*k + 19)*x^2 + (k - 3)^2*x^3)/(1 - x)^5. - Ilya Gutkovskiy, Apr 13 2016
LINKS
Michael De Vlieger, Table of n, a(n) for n = 0..10000
L. Euler, De mirabilibus proprietatibus numerorum pentagonalium, par. 29
L. Euler, On the remarkable properties of the pentagonal numbers, arXiv:math/0505373 [math.HO], 2005.
Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1)
FORMULA
a(n) = A000326(n)^2.
G.f.: x*(1+20*x+29*x^2+4*x^3)/(1-x)^5. [Colin Barker, Feb 14 2012]
From Ilya Gutkovskiy, Apr 13 2016: (Start)
E.g.f.: x*(4 + 46*x + 48*x^2 + 9*x^3)*exp(x)/4.
a(n) = 5*a(n-1) - 10*(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5). (End)
MATHEMATICA
LinearRecurrence[{5, -10, 10, -5, 1}, {0, 1, 25, 144, 484}, 32] (* Ilya Gutkovskiy, Apr 13 2016 *)
Table[(1/4) n^2 (3 n - 1)^2, {n, 0, 31}] (* Michael De Vlieger, Apr 13 2016 *)
PROG
(PARI) a(n) = (1/4)*n^2*(3*n-1)^2 \\ Altug Alkan, Apr 13 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Ralf Stephan, Nov 13 2004
STATUS
approved