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

Author

Ilya Gutkovskiy, Nov 26 2015

Keywords

• nonn
• easy

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

• 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).

Crossrefs

Cf. A172082.

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

Programs

Magma

[n*(n+1)*(n+2)*(9*n-7)/12: n in [0..50]]; // Vincenzo Librandi, Nov 27 2015

Mathematica

Table[n (n + 1) (n + 2) (9 n - 7)/12, {n, 0, 50}]

PARI

a(n)=n*(n+1)*(n+2)*(9*n-7)/12 \\ Charles R Greathouse IV, Jul 26 2016

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