A139577 a(n) = n*(2*n + 11).
0, 13, 30, 51, 76, 105, 138, 175, 216, 261, 310, 363, 420, 481, 546, 615, 688, 765, 846, 931, 1020, 1113, 1210, 1311, 1416, 1525, 1638, 1755, 1876, 2001, 2130, 2263, 2400, 2541, 2686, 2835, 2988, 3145, 3306, 3471, 3640, 3813, 3990
Offset: 0
Links
- Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
Programs
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Mathematica
s=0;lst={s};Do[s+=n++ +13;AppendTo[lst, s], {n, 0, 7!, 4}];lst (* Vladimir Joseph Stephan Orlovsky, Nov 19 2008 *) Table[n(2n+11),{n,0,50}] (* or *) LinearRecurrence[{3,-3,1},{0,13,30},50] (* Harvey P. Dale, Mar 17 2019 *) -
PARI
a(n)=n*(2*n+11) \\ Charles R Greathouse IV, Jun 17 2017
Formula
a(n) = 2*n^2 + 11*n.
a(n) = a(n-1) + 4*n + 9 (with a(0)=0). - Vincenzo Librandi, Nov 24 2010
From Elmo R. Oliveira, Nov 29 2024: (Start)
G.f.: x*(13 - 9*x)/(1-x)^3.
E.g.f.: exp(x)*x*(13 + 2*x).
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2. (End)