

A152773


3 times heptagonal numbers: a(n) = 3n(5n3)/2.


16



0, 3, 21, 54, 102, 165, 243, 336, 444, 567, 705, 858, 1026, 1209, 1407, 1620, 1848, 2091, 2349, 2622, 2910, 3213, 3531, 3864, 4212, 4575, 4953, 5346, 5754, 6177, 6615, 7068, 7536, 8019, 8517, 9030, 9558, 10101, 10659, 11232, 11820
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OFFSET

0,2


COMMENTS

Also the number of 6cycles in the (n+5)triangular honeycomb acute knight graph.  Eric W. Weisstein, Jun 25 2017


LINKS

Ivan Panchenko, Table of n, a(n) for n = 0..1000
Eric Weisstein's World of Mathematics, Graph Cycle
Index entries for linear recurrences with constant coefficients, signature (3,3,1).


FORMULA

a(n) = (15n^2  9n)/2 = A000566(n)*3.
a(n) = a(n1)+15*n12 with n>0, a(0)=0.  Vincenzo Librandi, Nov 26 2010
G.f.: 3*x*(1+4*x)/(1x)^3.  Bruno Berselli, Jan 21 2011
a(0)=0, a(1)=3, a(2)=21, a(n)=3*a(n1)3*a(n2)+a(n3).  Harvey P. Dale, May 08 2012
a(n) = n + A226489(n).  Bruno Berselli, Jun 11 2013


MATHEMATICA

Table[3 n (5 n  3)/2, {n, 0, 50}] (* Harvey P. Dale, May 08 2012 *)
LinearRecurrence[{3, 3, 1}, {0, 3, 21}, 50] (* Harvey P. Dale, May 08 2012 *)
CoefficientList[Series[((3 x^5 (1 + 4 x))/(1 + x)^3), {x, 0, 20}], x] (* Eric W. Weisstein, Jun 25 2017 *)


PROG

(PARI) a(n)=3*n*(5*n3)/2 \\ Charles R Greathouse IV, Sep 24 2015


CROSSREFS

Cf. A000566, A135706.
3 times ngonal numbers: A045943, A033428, A062741, A094159, A152751, A152759, A152767, A153783, A153448, A153875.
Cf. numbers of the form n*(n*kk+6))/2, this sequence is the case k=15: see Comments lines of A226492.
Cf. A002378 (3cycles in triangular honeycomb acute knight graph), A045943 (4cycles), A028896 (5cycles).
Sequence in context: A027499 A303834 A340687 * A039595 A033567 A181156
Adjacent sequences: A152770 A152771 A152772 * A152774 A152775 A152776


KEYWORD

nonn,easy


AUTHOR

Omar E. Pol, Dec 13 2008


STATUS

approved



