A164013 3 times centered triangular numbers: 9*n*(n+1)/2 + 3.
3, 12, 30, 57, 93, 138, 192, 255, 327, 408, 498, 597, 705, 822, 948, 1083, 1227, 1380, 1542, 1713, 1893, 2082, 2280, 2487, 2703, 2928, 3162, 3405, 3657, 3918, 4188, 4467, 4755, 5052, 5358, 5673, 5997, 6330, 6672, 7023, 7383, 7752
Offset: 0
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).
Programs
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Mathematica
LinearRecurrence[{3,-3,1},{3,12,30},50] (* Harvey P. Dale, Mar 26 2015 *) -
PARI
a(n)=9*binomial(n+1,2)+3 \\ Charles R Greathouse IV, Jul 17 2011
Formula
a(n) = a(n-1) + 9*n (with a(0)=3). - Vincenzo Librandi, Nov 30 2010
a(0)=3, a(1)=12, a(2)=30, a(n)=3*a(n-1)-3*a(n-2)+a(n-3). - Harvey P. Dale, Mar 26 2015
From G. C. Greubel, Sep 06 2017: (Start)
G.f.: 3*(1 + x + x^2)/(1 - x)^3.
E.g.f.: (3/2)*(2 + 6*x + 3*x^2)*exp(x). (End)