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) = 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
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
KEYWORD
easy,nonn
AUTHOR
Omar E. Pol, Dec 12 2008
STATUS
approved