

A152743


6 times pentagonal numbers: a(n) = 3*n*(3*n1).


12



0, 6, 30, 72, 132, 210, 306, 420, 552, 702, 870, 1056, 1260, 1482, 1722, 1980, 2256, 2550, 2862, 3192, 3540, 3906, 4290, 4692, 5112, 5550, 6006, 6480, 6972, 7482, 8010, 8556, 9120, 9702, 10302, 10920, 11556, 12210, 12882, 13572, 14280
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OFFSET

0,2


COMMENTS

a(n) is also the Wiener index of the windmill graph D(4,n). The windmill graph D(m,n) is the graph obtained by taking n copies of the complete graph K_m with a vertex in common (i.e. a bouquet of n pieces of K_m graphs). The Wiener index of a connected graph is the sum of distances between all unordered pairs of vertices in the graph. The Wiener index of D(m,n) is (1/2)n(m1)[(m1)(2n1)+1]. For the Wiener indices of D(3,n), D(5,n), and D(6,n) see A033991, A028994, and A180577, respectively.  Emeric Deutsch, Sep 21 2010
a(n+1) gives the number of edges in a hexagonlike honeycomb built from A003215(n) congruent regular hexagons (see link). Example: a hexagonlike honeycomb consisting of 7 congruent regular hexagons has 1 core hexagon inside a perimeter of six hexagons. The perimeter consists of 18 external edges. There are 6 edges shared by the perimeter hexagons. The core hexagon has 6 edges. a(2) is the total number of edges, i.e. 18 + 6 + 6 = 30.  Ivan N. Ianakiev, Mar 10 2015


LINKS

Ivan Panchenko, Table of n, a(n) for n = 0..1000
Ivan N. Ianakiev, Hexagonlike honeycomb built from regular congruent hexagons
Eric Weisstein's World of Mathematics, Windmill Graph
Index entries for linear recurrences with constant coefficients, signature (3, 3, 1).


FORMULA

a(n) = 9n^2  3n = A000326(n)*6.
a(n) = A049450(n)*3 = A062741(n)*2.  Omar E. Pol, Dec 15 2008
a(n) = a(n1)+18*n12 (with a(0)=0).  Vincenzo Librandi, Nov 26 2010
G.f.: ((6*x*(2*x+1))/(x1)^3).  Harvey P. Dale, Jun 30 2011
E.g.f.: 3*x*(2+3*x)*exp(x).  G. C. Greubel, Sep 01 2018


MAPLE

A152743:=n>3*n*(3*n1); seq(A152743(n), n=0..50); # Wesley Ivan Hurt, Jun 09 2014


MATHEMATICA

Table[3n(3n1), {n, 0, 40}] (* or *) LinearRecurrence[{3, 3, 1}, {0, 6, 30}, 40] (* Harvey P. Dale, Jun 30 2011 *)
CoefficientList[Series[6x (2x+1)/(x1)^3, {x, 0, 40}], x] (* Robert G. Wilson v, Mar 10 2015 *)


PROG

(MAGMA) [ 3*n*(3*n1) : n in [0..50] ]; // Wesley Ivan Hurt, Jun 09 2014
(PARI) a(n)=3*n*(3*n1) \\ Charles R Greathouse IV, Oct 07 2015


CROSSREFS

Cf. A000326, A152734, A152744, A049450, A062741, A033991, A028994, A180577.
Sequence in context: A277521 A163640 A199130 * A215906 A305163 A038039
Adjacent sequences: A152740 A152741 A152742 * A152744 A152745 A152746


KEYWORD

easy,nonn


AUTHOR

Omar E. Pol, Dec 12 2008


EXTENSIONS

Converted reference to link by Omar E. Pol, Oct 07 2010


STATUS

approved



