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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

Ivan Panchenko, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

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

Cf. A000384, A002939, A067239, A085250.

Sequence in context: A139279 A250257 A067239 * A121355 A227499 A168012

Adjacent sequences:  A152747 A152748 A152749 * A152751 A152752 A152753

KEYWORD

easy,nonn

AUTHOR

Omar E. Pol, Dec 12 2008

STATUS

approved

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Last modified November 21 16:27 EST 2017. Contains 295003 sequences.