OFFSET
0,2
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).
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
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 *)
PROG
(PARI) a(n)=n*(31*n+1)/2 \\ Charles R Greathouse IV, Jun 17 2017
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).
KEYWORD
nonn,easy
AUTHOR
STATUS
approved