A139580 a(n) = n*(2*n + 17).
0, 19, 42, 69, 100, 135, 174, 217, 264, 315, 370, 429, 492, 559, 630, 705, 784, 867, 954, 1045, 1140, 1239, 1342, 1449, 1560, 1675, 1794, 1917, 2044, 2175, 2310, 2449, 2592, 2739, 2890, 3045, 3204, 3367, 3534, 3705, 3880, 4059
Offset: 0
Links
- Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
Programs
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Mathematica
a[n_]:=Sum[4*i+15, {i, 1, n}]; (* Vladimir Joseph Stephan Orlovsky, Dec 04 2008 *) Table[n(2n+17),{n,0,50}] (* or *) LinearRecurrence[{3,-3,1},{0,19,42},50] (* Harvey P. Dale, Jul 07 2024 *) -
PARI
a(n)=n*(2*n+17) \\ Charles R Greathouse IV, Jun 17 2017
Formula
a(n) = 2*n^2 + 17*n.
a(n) = a(n-1) + 4*n + 15; a(0) = 0. - Vincenzo Librandi, Nov 24 2010
From Elmo R. Oliveira, Nov 29 2024: (Start)
G.f.: x*(19 - 15*x)/(1-x)^3.
E.g.f.: exp(x)*x*(19 + 2*x).
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2. (End)