A164016 6 times centered hexagonal numbers: 18*n*(n+1) + 6.

6, 42, 114, 222, 366, 546, 762, 1014, 1302, 1626, 1986, 2382, 2814, 3282, 3786, 4326, 4902, 5514, 6162, 6846, 7566, 8322, 9114, 9942, 10806, 11706, 12642, 13614, 14622, 15666, 16746, 17862, 19014, 20202, 21426, 22686, 23982, 25314

Offset

0,1

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).

Formula

a(n) = A003215(n)*6.

a(n) = a(n-1) + 36*n (with a(0)=6). - Vincenzo Librandi, Nov 30 2010

a(n) = 3*a(n-1)-3*a(n-2)+a(n-3) with a(0)=6, a(1)=42, a(2)=114. - Harvey P. Dale, Dec 16 2012

From G. C. Greubel, Sep 07 2017: (Start)

G.f.: 6*(1 + 4*x + x^2)/(1 - x)^3.

E.g.f.: 6*(1 + 6*x + 3*x^2)*exp(x). (End)

Mathematica

Table[18n(n+1)+6, {n, 0, 40}] (* or *) LinearRecurrence[{3, -3, 1}, {6, 42, 114}, 40] (* Harvey P. Dale, Dec 16 2012 *)

Prog

(PARI) a(n)=18*n*(n+1)+6 \\ Charles R Greathouse IV, Jul 17 2011

Crossrefs

Cf. A003215, A152746, A164013, A108099, A164015.

Sequence in context: A211616 A153786 A256833 * A147811 A046763 A199905

Adjacent sequences: A164013 A164014 A164015 * A164017 A164018 A164019

Keyword

easy,nonn

Author

Omar E. Pol, Nov 07 2009

Status

approved