OFFSET
0,2
REFERENCES
V. van der Noort and N. J. A. Sloane, Paper in preparation, 2007.
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) = 24*n + a(n-1) - 14 for n>0, a(0)=0. - Vincenzo Librandi, Nov 23 2010
From Harvey P. Dale, Nov 19 2011: (Start)
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2, a(0)=0, a(1)=10, a(2)=44.
G.f.: (10*x + 14*x^2)/(1 - x)^3. (End)
From Ilya Gutkovskiy, Dec 04 2016: (Start)
Sum_{n>=1} 1/a(n) = (4*log(2) + 3*log(3) - sqrt(3)*Pi)/4 = 0.15675687388...
E.g.f.: 2*x*(5 + 6*x)*exp(x). (End)
a(n) = Sum_{i=n..5*n-1} i. - Wesley Ivan Hurt, Dec 04 2016
MAPLE
MATHEMATICA
Table[2n(6n-1), {n, 0, 50}] (* or *) LinearRecurrence[{3, -3, 1}, {0, 10, 44}, 50] (* Harvey P. Dale, Nov 19 2011 *)
PROG
(Magma) [2*n*(6*n-1) : n in [0..50]]; // Wesley Ivan Hurt, Dec 03 2016
(PARI) a(n)=2*n*(6*n-1) \\ Charles R Greathouse IV, Jun 16 2017
(Sage) [2*binomial(6*n, 2)/3 for n in (0..50)] # G. C. Greubel, Jan 29 2020
(GAP) List([0..50], n-> 2*Binomial(6*n, 2)/3 ); # G. C. Greubel, Jan 29 2020
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Mar 21 2007
STATUS
approved