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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
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
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
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