A264895 a(n) = n*(4*n - 3)*(16*n^2 - 12*n - 3).

0, 1, 370, 2835, 10660, 28645, 63126, 121975, 214600, 351945, 546490, 812251, 1164780, 1621165, 2200030, 2921535, 3807376, 4880785, 6166530, 7690915, 9481780, 11568501, 13981990, 16754695, 19920600, 23515225, 27575626, 32140395, 37249660, 42945085, 49269870

Offset: 0

Author

Ilya Gutkovskiy, Nov 27 2015

Keywords

• nonn
• easy

Comments

Doubly 10-gonal (or decagonal) numbers.

Links

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

Crossrefs

Cf. A001107, A002817, A000583, A232713, A063249.

Programs

Magma

[n*(4*n - 3)*(16*n^2 - 12*n - 3): n in [0..30]]; // Vincenzo Librandi, Nov 28 2015

Mathematica

Table[n (4 n - 3) (16 n^2 - 12 n - 3), {n, 0, 30}]
LinearRecurrence[{5,-10,10,-5,1}, {0, 1, 370, 2835, 10660}, 50] (* G. C. Greubel, Sep 07 2018 *)

PARI

vector(100, n, n--; n*(4*n-3)*(16*n^2-12*n-3)) \\ Altug Alkan, Nov 27 2015

Formula

G.f.: x*(1 + 365*x + 995*x^2 + 175*x^3)/(1 - x)^5.

a(n) = A001107(A001107(n)).

Sum_{n>0} 1/a(n) = (sqrt(21)*gamma + sqrt(21)*polygamma(0, 1/4) - 3*polygamma(0, (1/8)*(5 - sqrt(21))) + 3*polygamma(0, (1/8)*(5 + sqrt(21))))/(9*sqrt(21))= 1.00322253307732984...., where gamma is the Euler-Mascheroni constant (A001620), and polygamma is the derivative of the logarithm of the gamma function.