A153786 6 times heptagonal numbers: a(n) = 3*n*(5*n-3).

0, 6, 42, 108, 204, 330, 486, 672, 888, 1134, 1410, 1716, 2052, 2418, 2814, 3240, 3696, 4182, 4698, 5244, 5820, 6426, 7062, 7728, 8424, 9150, 9906, 10692, 11508, 12354, 13230, 14136, 15072, 16038, 17034, 18060, 19116, 20202, 21318

Offset

0,2

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

a(n) = 15*n^2 - 9*n = A000566(n)*6 = A135706(n)*3 = A152773(n)*2.

a(n) = 30*n + a(n-1) - 24 for n>0, a(0)=0. - Vincenzo Librandi, Aug 03 2010

From G. C. Greubel, Aug 28 2016: (Start)

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).

G.f.: 6*x*(1 + 4*x))/(1 - x)^3.

E.g.f.: 3*x*(2 + 5*x)*exp(x). (End)

Mathematica

s=0; lst={s}; Do[s+=n; AppendTo[lst, s], {n, 6, 8!, 30}]; lst (* Vladimir Joseph Stephan Orlovsky, Apr 03 2009 *)
Table[ 3*n*(5*n-3), {n, 0, 25}] (* or *) LinearRecurrence[{3, -3, 1}, {0, 6, 42}, 25] (* G. C. Greubel, Aug 28 2016 *)

Prog

(PARI) a(n) = 3*n*(5*n-3); \\ Michel Marcus, Aug 28 2016

Crossrefs

Cf. A000566, A135706, A152773, A152777, A153785.

Sequence in context: A043896 A044489 A211616 * A256833 A164016 A147811

Adjacent sequences: A153783 A153784 A153785 * A153787 A153788 A153789

Keyword

nonn,easy

Author

Omar E. Pol, Jan 02 2009

Status

approved