

A049453


Second pentagonal numbers with even index: a(n) = n*(6*n+1).


23



0, 7, 26, 57, 100, 155, 222, 301, 392, 495, 610, 737, 876, 1027, 1190, 1365, 1552, 1751, 1962, 2185, 2420, 2667, 2926, 3197, 3480, 3775, 4082, 4401, 4732, 5075, 5430, 5797, 6176, 6567, 6970, 7385, 7812, 8251, 8702, 9165, 9640, 10127, 10626
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,2


COMMENTS

Number of edges in the join of the complete tripartite graph of order 3n and the cycle graph of order n, K_n,n,n * C_n  Roberto E. Martinez II, Jan 07 2002
Sequence found by reading the line (one of the diagonal axes) from 0, in the direction 0, 7, ..., in the square spiral whose vertices are the generalized pentagonal numbers A001318.  Omar E. Pol, Sep 08 2011
First bisection of A036498.  Bruno Berselli, Nov 25 2012


LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,3,1).


FORMULA

G.f.: x*(7+5*x)/(1x)^3.
a(n) = 12*n + a(n1)  5 with n>0, a(0)=0.  Vincenzo Librandi, Aug 06 2010
a(n) = 3*a(n1)  3*a(n2) + a(n3).  G. C. Greubel, Jun 07 2017


MAPLE

seq(binomial(6*n+1, 2)/3, n=0..42); # Zerinvary Lajos, Jan 21 2007


MATHEMATICA

s=0; lst={s}; Do[s+=n++ +7; AppendTo[lst, s], {n, 0, 7!, 12}]; lst (* Vladimir Joseph Stephan Orlovsky, Nov 16 2008 *)
Table[n*(6*n + 1), {n, 0, 50}] (* G. C. Greubel, Jun 07 2017 *)


PROG

(PARI) x='x+O('x^50); concat([0], Vec(x*(7+5*x)/(1x)^3)) \\ G. C. Greubel, Jun 07 2017


CROSSREFS

Cf. A001318, A005449, A033568, A033570, A036498, A049452, A185019, A194454.
Cf. A254963 (comment).
Sequence in context: A274268 A059376 A206481 * A231888 A211645 A171340
Adjacent sequences: A049450 A049451 A049452 * A049454 A049455 A049456


KEYWORD

nonn,easy


AUTHOR

Joe Keane (jgk(AT)jgk.org)


STATUS

approved



