A100176 Structured octagonal prism numbers.

1, 16, 63, 160, 325, 576, 931, 1408, 2025, 2800, 3751, 4896, 6253, 7840, 9675, 11776, 14161, 16848, 19855, 23200, 26901, 30976, 35443, 40320, 45625, 51376, 57591, 64288, 71485, 79200, 87451, 96256, 105633, 115600, 126175, 137376, 149221, 161728, 174915, 188800

Offset: 1

Author

James A. Record (james.record(AT)gmail.com), Nov 07 2004

Keywords

• nonn
• easy

Comments

Number of divisors of 120^(n-1). - J. Lowell, Aug 30 2008

Partial sums of A214675. - J. M. Bergot, Jul 08 2013

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..10000
• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Crossrefs

Cf. A100177 (structured prisms), A100145 (for more on structured numbers).

Cf. similar sequences, with the formula (k*n - k + 2)*n^2/2, listed in A262000.

Cf. A000567, A016777, A214675.

Programs

Magma

[3*n^3-2*n^2: n in [1..50] ]; // Vincenzo Librandi, Aug 02 2011

Maple

[seq(3*n^3-2*n^2,n=1..47)]; # Zerinvary Lajos, Jun 29 2006

Mathematica

f[n_] := 3 n^3 - 2 n^2; Table[f[n], {n, 0, 50}] (* Vladimir Joseph Stephan Orlovsky, Apr 27 2010 *)

PARI

a(n)=3*n^3-2*n^2 \\ Charles R Greathouse IV, Aug 10 2017

Formula

a(n) = 3*n^3 - 2*n^2.

G.f.: x*(1+12*x+5*x^2)/(1-x)^4. - Colin Barker, Jun 08 2012

a(n) = Sum_{i=0..n-1} n*(6*i+1). - Bruno Berselli, Sep 08 2015

Sum_{n>=1} 1/a(n) = sqrt(3)*Pi/8 - Pi^2/12 + 9*log(3)/8 = 1.0936465529153418... . - Vaclav Kotesovec, Oct 04 2016

a(n) = n*A000567(n) = n^2 * A016777(n-1). - Bruce J. Nicholson, Aug 10 2017

From Elmo R. Oliveira, Aug 06 2025: (Start)

E.g.f.: exp(x)*x*(1 + 7*x + 3*x^2).

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). (End)

Extensions

More terms from Zerinvary Lajos, Jun 29 2006