A022289 a(n) = n*(31*n + 1)/2.

0, 16, 63, 141, 250, 390, 561, 763, 996, 1260, 1555, 1881, 2238, 2626, 3045, 3495, 3976, 4488, 5031, 5605, 6210, 6846, 7513, 8211, 8940, 9700, 10491, 11313, 12166, 13050, 13965, 14911, 15888, 16896, 17935

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. similar sequences of the form n*((2*k+1)*n + 1)/2: A000217 (k=0), A005449 (k=1), A005475 (k=2), A022265 (k=3), A022267 (k=4), A022269 (k=5), A022271 (k=6), A022273 (k=7), A022275 (k=8), A022277 (k=9), A022279 (k=10), A022281 (k=11), A022283 (k=12), A022285 (k=13), A022287 (k=14), this sequence (k=15).

Programs

Mathematica

Table[n (31 n + 1)/2, {n, 0, 40}] (* Bruno Berselli, Oct 13 2016 *)
LinearRecurrence[{3,-3,1},{0,16,63},40] (* Harvey P. Dale, Aug 10 2019 *)

PARI

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

Formula

a(n) = 31*n + a(n-1) - 15, for n>0, a(0)=0. - Vincenzo Librandi, Aug 04 2010

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

a(n) = A000217(16*n) - A000217(15*n). In general, n*((2*k+1)*n + 1)/2 = A000217((k+1)*n) - A000217(k*n). - Bruno Berselli, Oct 13 2016

E.g.f.: (x/2)*(31*x + 32)*exp(x). - G. C. Greubel, Aug 23 2017