

A264853


a(n) = n*(n + 1)*(5*n^2 + 5*n  4)/12.


2



0, 1, 13, 56, 160, 365, 721, 1288, 2136, 3345, 5005, 7216, 10088, 13741, 18305, 23920, 30736, 38913, 48621, 60040, 73360, 88781, 106513, 126776, 149800, 175825, 205101, 237888, 274456, 315085, 360065, 409696, 464288, 524161, 589645, 661080, 738816, 823213, 914641
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OFFSET

0,3


COMMENTS

Partial sums of centered 10gonal (or decagonal) pyramidal numbers.
Subsequence of A204221. In fact, a(n) is of the form (k^21)/15 for k = 5*n*(n+1)/21.  Bruno Berselli, Nov 27 2015


LINKS

Table of n, a(n) for n=0..38.
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(n1)  10*a(n2) + 10*a(n3)  5*a(n4) + a(n5).  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*n4)/12: n in [0..50]]; // Vincenzo Librandi, Nov 27 2015
(PARI) a(n)=n*(n+1)*(5*n^2+5*n4)/12 \\ Charles R Greathouse IV, Jul 26 2016


CROSSREFS

Cf. A004466, A204221.
Cf. similar sequences listed in A264854.
Sequence in context: A290396 A061161 A212053 * A210290 A007202 A222161
Adjacent sequences: A264850 A264851 A264852 * A264854 A264855 A264856


KEYWORD

nonn,easy


AUTHOR

Ilya Gutkovskiy, Nov 26 2015


STATUS

approved



