A022277 a(n) = n*(19*n + 1)/2.

0, 10, 39, 87, 154, 240, 345, 469, 612, 774, 955, 1155, 1374, 1612, 1869, 2145, 2440, 2754, 3087, 3439, 3810, 4200, 4609, 5037, 5484, 5950, 6435, 6939, 7462, 8004, 8565, 9145, 9744, 10362, 10999, 11655, 12330, 13024, 13737, 14469, 15220, 15990, 16779, 17587, 18414

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. A022276.

Cf. similar sequences listed in A022289.

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, 100}] (* Vladimir Joseph Stephan Orlovsky, Mar 07 2011 *)
CoefficientList[Series[x (10 + 9 x) / (1 - x)^3, {x, 0, 40}], x] (* Vincenzo Librandi, Mar 31 2015 *)
LinearRecurrence[{3,-3,1},{0,10,39},50] (* Harvey P. Dale, May 02 2021 *)

PARI

a(n)=n*(19*n+1)/2 \\ Charles R Greathouse IV, Mar 07 2011

Formula

a(n) = 19*n + a(n-1) - 9 for n>0, a(0)=0. - Vincenzo Librandi, Aug 04 2010

G.f.: x*(10 + 9*x)/(1 - x)^3. - Vincenzo Librandi, Mar 31 2015

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>2. - Vincenzo Librandi, Mar 31 2015

a(n) = A022276(-n). - Bruno Berselli, Apr 01 2015

a(n) = A000217(10*n) - A000217(9*n). - Bruno Berselli, Oct 13 2016

E.g.f.: (x/2)*(19*x + 20)*exp(x). - G. C. Greubel, Aug 23 2017

Extensions

More terms from Vincenzo Librandi, Mar 31 2015