A164013 3 times centered triangular numbers: 9*n*(n+1)/2 + 3.

3, 12, 30, 57, 93, 138, 192, 255, 327, 408, 498, 597, 705, 822, 948, 1083, 1227, 1380, 1542, 1713, 1893, 2082, 2280, 2487, 2703, 2928, 3162, 3405, 3657, 3918, 4188, 4467, 4755, 5052, 5358, 5673, 5997, 6330, 6672, 7023, 7383, 7752

Offset

0,1

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Formula

a(n) = a(n-1) + 9*n (with a(0)=3). - Vincenzo Librandi, Nov 30 2010

a(0)=3, a(1)=12, a(2)=30, a(n)=3*a(n-1)-3*a(n-2)+a(n-3). - Harvey P. Dale, Mar 26 2015

From G. C. Greubel, Sep 06 2017: (Start)

G.f.: 3*(1 + x + x^2)/(1 - x)^3.

E.g.f.: (3/2)*(2 + 6*x + 3*x^2)*exp(x). (End)

Mathematica

LinearRecurrence[{3, -3, 1}, {3, 12, 30}, 50] (* Harvey P. Dale, Mar 26 2015 *)

Prog

(PARI) a(n)=9*binomial(n+1, 2)+3 \\ Charles R Greathouse IV, Jul 17 2011

Crossrefs

Cf. A005448, A045943, A108099, A164015, A164016.

Sequence in context: A101459 A051408 A331080 * A057671 A027480 A135503

Adjacent sequences: A164010 A164011 A164012 * A164014 A164015 A164016

Keyword

easy,nonn

Author

Omar E. Pol, Nov 07 2009

Status

approved