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A153786
6 times heptagonal numbers: a(n) = 3*n*(5*n-3).
1
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
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
KEYWORD
nonn,easy
AUTHOR
Omar E. Pol, Jan 02 2009
STATUS
approved