A022285 a(n) = n*(27*n + 1)/2.

0, 14, 55, 123, 218, 340, 489, 665, 868, 1098, 1355, 1639, 1950, 2288, 2653, 3045, 3464, 3910, 4383, 4883, 5410, 5964, 6545, 7153, 7788, 8450, 9139, 9855, 10598, 11368, 12165, 12989, 13840, 14718, 15623

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 listed in A022289.

Programs

Maple

A022285:=n->n*(27*n+1)/2; seq(A022285(k), k=0..100); # Wesley Ivan Hurt, Nov 04 2013

Mathematica

Table[n (27 n + 1)/2, {n, 0, 40}] (* or *) LinearRecurrence[{3, -3, 1}, {0, 14, 55}, 40] (* Harvey P. Dale, Sep 20 2011 *)

PARI

a(n)=n*(27*n+1)/2 \\ Charles R Greathouse IV, Jun 17 2017

Formula

a(n) = a(n-1) + 27*n - 13 for n>0, a(0)=0. - Vincenzo Librandi, Aug 04 2010

a(0)=0, a(1)=14, a(2)=55; for n>2, a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). -Harvey P. Dale, Sep 20 2011

G.f.: x*(13*x + 14)/(1-x)^3. - Harvey P. Dale, Sep 20 2011

a(n) = 12/(n+2)!*Sum_{j=0..n} (-1)^(n-j)*binomial(n,j)*(j+n)^(n+2). - Vladimir Kruchinin, Jun 04 2013

a(n) = A000217(14*n) - A000217(13*n). - Bruno Berselli, Oct 13 2016

E.g.f.: (x/2)*(27*x + 28)*exp(x). - G. C. Greubel, Aug 23 2017