A264892 a(n) = n*(3*n - 2)*(9*n^2 - 6*n - 2).

0, 1, 176, 1281, 4720, 12545, 27456, 52801, 92576, 151425, 234640, 348161, 498576, 693121, 939680, 1246785, 1623616, 2080001, 2626416, 3273985, 4034480, 4920321, 5944576, 7120961, 8463840, 9988225, 11709776, 13644801, 15810256, 18223745, 20903520

Offset: 0

Author

Ilya Gutkovskiy, Nov 27 2015

Keywords

• nonn
• easy

Comments

Doubly octagonal numbers.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..5000
• OEIS Wiki, Figurate numbers
• Eric Weisstein's World of Mathematics, Octagonal Number
• Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1)

Crossrefs

Cf. A000567, A002817, A000583, A232713, A063249.

Programs

Magma

[n*(3*n-2)*(9*n^2-6*n-2): n in [0..30]]; // Vincenzo Librandi, Nov 28 2015

Mathematica

Table[n (3 n - 2) (9 n^2 - 6 n - 2), {n, 0, 30}]

PARI

concat(0, Vec(x*(1+171*x+411*x^2+65*x^3)/(1-x)^5 + O(x^100))) \\ Altug Alkan, Nov 27 2015

Formula

G.f.: x*(1 + 171*x + 411*x^2 + 65*x^3)/(1 - x)^5.

a(n) = A000567(A000567(n)).

Sum_{n>0} 1/a(n) = (sqrt(3)*gamma + sqrt(3)*polygamma(0, 1/3) - polygamma(0, (1/3)*(2 - sqrt(3))) + polygamma(0, (1/3)*(2 + sqrt(3))))/(4*sqrt(3)) = 1.006842786293...,where gamma is the Euler-Mascheroni constant (A001620), and polygamma is the derivative of the logarithm of the gamma function.