

A152746


Six times hexagonal numbers: 6*n*(2*n1).


14



0, 6, 36, 90, 168, 270, 396, 546, 720, 918, 1140, 1386, 1656, 1950, 2268, 2610, 2976, 3366, 3780, 4218, 4680, 5166, 5676, 6210, 6768, 7350, 7956, 8586, 9240, 9918, 10620, 11346, 12096, 12870, 13668, 14490, 15336, 16206, 17100
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OFFSET

0,2


COMMENTS

Sequence found by reading the line from 0, in the direction 0, 6, ..., in the square spiral whose vertices are the generalized octagonal numbers A001082.  Omar E. Pol, Sep 18 2011
a(n) is the number of walks on a cubic lattice of n dimensions that return to the origin, not necessarily for the first time, after 4 steps.  Shel Kaphan, Mar 20 2023


LINKS



FORMULA

G.f.: 6*x*(1+3*x)/(1x)^3.
E.g.f.: 6*x*(1+2*x)*exp(x). (End)
Sum_{n>=1} 1/a(n) = log(2)/3.
Sum_{n>=1} (1)^(n+1)/a(n) = Pi/12  log(2)/6. (End)


MATHEMATICA

6*PolygonalNumber[6, Range[0, 40]] (* The program uses the PolygonalNumber function from Mathematica version 10 *) (* Harvey P. Dale, Mar 04 2016 *)
LinearRecurrence[{3, 3, 1}, {0, 6, 36}, 50] (* or *) Table[6*n*(2*n1), {n, 0, 50}] (* G. C. Greubel, Sep 01 2018 *)


PROG

(Magma) [6*n*(2*n1): n in [0..50]]; // G. C. Greubel, Sep 01 2018


CROSSREFS



KEYWORD

easy,nonn,walk


AUTHOR



STATUS

approved



