A022276 a(n) = n*(19*n - 1)/2.

0, 9, 37, 84, 150, 235, 339, 462, 604, 765, 945, 1144, 1362, 1599, 1855, 2130, 2424, 2737, 3069, 3420, 3790, 4179, 4587, 5014, 5460, 5925, 6409, 6912, 7434, 7975, 8535, 9114, 9712, 10329, 10965, 11620, 12294, 12987, 13699, 14430, 15180, 15949, 16737, 17544, 18370

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..5000
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A000217, A022277.

Cf. similar sequences listed in A022288.

Programs

Magma

[n*(19*n - 1)/2: n in [0..45]]; // Vincenzo Librandi, Mar 31 2015

Mathematica

Table[n (19 n - 1)/2, {n, 0, 40}] (* Bruno Berselli, Mar 12 2015 *)
CoefficientList[Series[x (9 + 10 x) / (1 - x)^3, {x, 0, 40}], x] (* Vincenzo Librandi, Mar 31 2015 *)
LinearRecurrence[{3,-3,1},{0,9,37},50] (* Harvey P. Dale, Jul 25 2021 *)

PARI

a(n)=n*(19*n-1)/2 \\ Charles R Greathouse IV, Jun 17 2017

Formula

a(n) = 19*n + a(n-1) - 10 for n>0, a(0)=0. - Vincenzo Librandi, Aug 04 2010

From Vincenzo Librandi, Mar 31 2015: (Start)

G.f.: x*(9 + 10*x)/(1 - x)^3.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>2. (End)

a(n) = A022277(-n). - Bruno Berselli, Apr 01 2015

a(n) = A000217(10*n-1) - A000217(9*n-1). - Bruno Berselli, Oct 17 2016

E.g.f.: (x/2)*(19*x + 18)*exp(x). - G. C. Greubel, Aug 23 2017

Extensions

More terms from Vincenzo Librandi, Mar 31 2015