A022288 a(n) = n*(31*n-1)/2.

0, 15, 61, 138, 246, 385, 555, 756, 988, 1251, 1545, 1870, 2226, 2613, 3031, 3480, 3960, 4471, 5013, 5586, 6190, 6825, 7491, 8188, 8916, 9675, 10465, 11286, 12138, 13021, 13935, 14880, 15856, 16863, 17901

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A000217, A022289.

Cf. similar sequences of the form n*((2*k+1)*n - 1)/2: A161680 (k=0), A000326 (k=1), A005476 (k=2), A022264 (k=3), A022266 (k=4), A022268 (k=5), A022270 (k=6), A022272 (k=7), A022274 (k=8), A022276 (k=9), A022278 (k=10), A022280 (k=11), A022282 (k=12), A022284 (k=13), A022286 (k=14), this sequence (k=15).

Programs

Mathematica

Table[n (31 n - 1)/2, {n, 0, 40}] (* or *) LinearRecurrence[{3, -3, 1}, {0, 15, 61}, 40] (* Harvey P. Dale, Mar 31 2014 *)

PARI

a(n)=n*(31*n-1)/2 \\ Charles R Greathouse IV, Jun 17 2017

Formula

a(n) = 31*n + a(n-1) - 16 for n>0, a(0)=0. - Vincenzo Librandi, Aug 04 2010

a(0)=0, a(1)=15, a(2)=61; for n>2, a(n) = 3*a(n-1)-3*a(n-2)+a(n-3). - Harvey P. Dale, Mar 31 2014

G.f.: x*(15 + 16*x)/(1 - x)^3. - R. J. Mathar, Sep 02 2016

a(n) = A000217(16*n-1) - A000217(15*n-1). In general, n*((2*k+1)*n - 1)/2 = A000217((k+1)*n-1) - A000217(k*n-1), and the ordinary generating function is x*(k + (k+1)*x)/(1 - x)^3. - Bruno Berselli, Oct 14 2016

E.g.f.: (x/2)*(31*x + 30)*exp(x). - G. C. Greubel, Aug 24 2017