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A152750 Eight times hexagonal numbers: 8*n*(2*n-1). 5
0, 8, 48, 120, 224, 360, 528, 728, 960, 1224, 1520, 1848, 2208, 2600, 3024, 3480, 3968, 4488, 5040, 5624, 6240, 6888, 7568, 8280, 9024, 9800, 10608, 11448, 12320, 13224, 14160, 15128, 16128, 17160, 18224, 19320, 20448, 21608, 22800, 24024, 25280, 26568 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
Equals Engel expansion of cosh(1/2), except first member (see A067239).
Also sequence found by reading the line from 0, in the direction 0, 8, ..., in the square spiral whose vertices are the generalized decagonal numbers A074377. - Omar E. Pol, Sep 18 2011
a(n) = the sum of the edges of a rectangular prism having edges 2*(n-1)*n, n^2-(n-1)^2 and n^2 + (n-1)^2. - J. M. Bergot, Apr 24 2014
LINKS
FORMULA
a(n) = 16n^2 - 8n = A000384(n)*8 = A002939(n)*4 = A085250(n)*2.
a(n) = A067239(n), for n>0.
a(n) = a(n-1)+32*n-24 (with a(0)=0). - Vincenzo Librandi, Nov 26 2010
From Colin Barker, Sep 25 2016: (Start)
a(n) = 3*a(n-1)-3*a(n-2)+a(n-3) for n>2.
G.f.: 8*x*(1+3*x) / (1-x)^3.
(End)
Sum_{n>=1} 1/a(n) = log(2)/4. - Vaclav Kotesovec, Sep 25 2016
MAPLE
A152750:=n->8*n*(2*n-1); seq(A152750(n), n=0..50); # Wesley Ivan Hurt, Jun 09 2014
MATHEMATICA
Table[8*n*(2*n - 1), {n, 0, 50}] (* Wesley Ivan Hurt, Jun 09 2014 *)
PROG
(Magma) [ 8*n*(2*n-1) : n in [0..50] ]; // Wesley Ivan Hurt, Jun 09 2014
(PARI) concat(0, Vec(8*x*(1+3*x)/(1-x)^3 + O(x^50))) \\ Colin Barker, Sep 25 2016
CROSSREFS
Sequence in context: A139279 A250257 A067239 * A121355 A227499 A168012
KEYWORD
easy,nonn
AUTHOR
Omar E. Pol, Dec 12 2008
STATUS
approved

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Last modified March 28 22:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)