A022270 a(n) = n*(13*n - 1)/2.

0, 6, 25, 57, 102, 160, 231, 315, 412, 522, 645, 781, 930, 1092, 1267, 1455, 1656, 1870, 2097, 2337, 2590, 2856, 3135, 3427, 3732, 4050, 4381, 4725, 5082, 5452, 5835, 6231, 6640, 7062, 7497, 7945, 8406, 8880, 9367, 9867, 10380, 10906, 11445

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, A022271.

Cf. similar sequences listed in A022288.

Programs

Magma

[n*(13*n - 1)/2: n in [0..45]]; // Vincenzo Librandi, Mar 31 2015

Mathematica

Table[n (13 n - 1)/2, {n, 0, 40}] (* or *) LinearRecurrence[{3,-3,1},{0,6,25},40] (* Harvey P. Dale, Dec 02 2011 *)
CoefficientList[Series[x (6 + 7 x) / (1 - x)^3, {x, 0, 40}], x] (* Vincenzo Librandi, Mar 31 2015 *)

PARI

A022270(n) = n*(13*n-1)/2 \\ Michael B. Porter, Mar 12 2010

Formula

a(n) = 13*n + a(n-1) - 7 for n>0, a(0)=0. - Vincenzo Librandi, Aug 04 2010

a(0)=0, a(1)=6, a(2)=25; for n>2, a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Harvey P. Dale, Dec 02 2011

G.f.: x*(6 + 7*x)/(1 - x)^3. - Vincenzo Librandi, Mar 31 2015

a(n) = A022271(-n). - Bruno Berselli, Mar 31 2015

a(n) = A000217(7*n-1) - A000217(6*n-1). - Bruno Berselli, Oct 17 2016

E.g.f.: (x/2)*(13*x + 12)*exp(x). - G. C. Greubel, Aug 23 2017

Extensions

More terms from Vincenzo Librandi, Mar 31 2015