A264852 a(n) = n*(n + 1)*(n + 2)*(9*n - 7)/12.

0, 1, 22, 100, 290, 665, 1316, 2352, 3900, 6105, 9130, 13156, 18382, 25025, 33320, 43520, 55896, 70737, 88350, 109060, 133210, 161161, 193292, 230000, 271700, 318825, 371826, 431172, 497350, 570865, 652240, 742016, 840752, 949025, 1067430, 1196580, 1337106

Offset

0,3

Comments

Partial sums of 20-gonal (or icosagonal) pyramidal numbers. Therefore, this is the case k=9 of the general formula n*(n + 1)*(n + 2)*(k*n - k + 2)/12, which is related to 2*(k+1)-gonal pyramidal numbers.

Links

Table of n, a(n) for n=0..36.

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 + 17*x)/(1 - x)^5.

a(n) = Sum_{k = 0..n} A172082(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) (n + 2) (9 n - 7)/12, {n, 0, 50}]

Prog

(Magma) [n*(n+1)*(n+2)*(9*n-7)/12: n in [0..50]]; // Vincenzo Librandi, Nov 27 2015
(PARI) a(n)=n*(n+1)*(n+2)*(9*n-7)/12 \\ Charles R Greathouse IV, Jul 26 2016

Crossrefs

Cf. A172082.

Cf. similar sequences with formula n*(n+1)*(n+2)*(k*n-k+2)/12 listed in A264850.

Sequence in context: A026909 A262914 A262329 * A044273 A044654 A156795

Adjacent sequences: A264849 A264850 A264851 * A264853 A264854 A264855

Keyword

nonn,easy

Author

Ilya Gutkovskiy, Nov 26 2015

Status

approved