OFFSET
0,3
COMMENTS
Partial sums of centered 10-gonal (or decagonal) pyramidal numbers.
Subsequence of A204221. In fact, a(n) is of the form (k^2-1)/15 for k = 5*n*(n+1)/2-1. - Bruno Berselli, Nov 27 2015
LINKS
OEIS Wiki, Figurate numbers
Eric Weisstein's World of Mathematics, Pyramidal Number
Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
FORMULA
G.f.: x*(1 + 8*x + x^2)/(1 - x)^5.
a(n) = Sum_{k = 0..n} A004466(k).
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5). - Vincenzo Librandi, Nov 27 2015
MATHEMATICA
Table[n (n + 1) (5 n^2 + 5 n - 4)/12, {n, 0, 50}]
LinearRecurrence[{5, -10, 10, -5, 1}, {0, 1, 13, 56, 160}, 40] (* Harvey P. Dale, Aug 14 2017 *)
PROG
(Magma) [n*(n+1)*(5*n^2+5*n-4)/12: n in [0..50]]; // Vincenzo Librandi, Nov 27 2015
(PARI) a(n)=n*(n+1)*(5*n^2+5*n-4)/12 \\ Charles R Greathouse IV, Jul 26 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Ilya Gutkovskiy, Nov 26 2015
STATUS
approved