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

0,2

Links

Table of n, a(n) for n=0..41.

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

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)

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 *)

Prog

(PARI) a(n)=n*(2*n+17) \\ Charles R Greathouse IV, Jun 17 2017

Crossrefs

Cf. A014105, A014106, A033537, A130861, A139576, A139577, A139578, A139579, A139581.

Sequence in context: A225583 A180932 A140603 * A156897 A094841 A001986

Adjacent sequences: A139577 A139578 A139579 * A139581 A139582 A139583

Keyword

easy,nonn

Author

Omar E. Pol, May 19 2008

Status

approved