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A100176 Structured octagonal prism numbers. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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).

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

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 *)

PROG

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

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

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.

Sequence in context: A066391 A022289 A143860 * A060091 A076751 A215969

Adjacent sequences:  A100173 A100174 A100175 * A100177 A100178 A100179

KEYWORD

nonn,easy

AUTHOR

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

EXTENSIONS

More terms from Zerinvary Lajos, Jun 29 2006

STATUS

approved

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Last modified October 21 16:50 EDT 2019. Contains 328302 sequences. (Running on oeis4.)