A022275 a(n) = n*(17*n + 1)/2.

0, 9, 35, 78, 138, 215, 309, 420, 548, 693, 855, 1034, 1230, 1443, 1673, 1920, 2184, 2465, 2763, 3078, 3410, 3759, 4125, 4508, 4908, 5325, 5759, 6210, 6678, 7163, 7665, 8184, 8720, 9273, 9843, 10430, 11034, 11655, 12293, 12948, 13620, 14309, 15015

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. A022274.

Cf. similar sequences listed in A022289.

Programs

Magma

[n*(17*n + 1)/2: n in [0..45]]; // Vincenzo Librandi, Mar 31 2015

Mathematica

Table[n (17 n + 1)/2, {n, 0, 40}] (* or *) LinearRecurrence[{3, -3, 1}, {0, 9, 35}, 40] (* Harvey P. Dale, May 06 2013 *)
CoefficientList[Series[x (9 + 8 x) / (1 - x)^3, {x, 0, 40}], x] (* Vincenzo Librandi, Mar 31 2015 *)

PARI

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

Formula

a(n) = 17*n + a(n-1) - 8 for n>0, a(0)=0. - Vincenzo Librandi, Aug 04 2010

a(0)=0, a(1)=9, a(2)=35; for n>2, a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Harvey P. Dale, May 06 2013

G.f.: x*(9+8*x)/(1-x)^3. - Vincenzo Librandi, Mar 31 2015

a(n) = A022274(-n). - Bruno Berselli, Mar 31 2015

a(n) = A000217(9*n) - A000217(8*n). - Bruno Berselli, Oct 13 2016

E.g.f.: (x/2)*(17*x + 18)*exp(x). - G. C. Greubel, Aug 23 2017

Extensions

More terms from Vincenzo Librandi, Mar 31 2015