A016790 a(n) = (3n+2)^2.

1, 4, 25, 64, 121, 196, 289, 400, 529, 676, 841, 1024, 1225, 1444, 1681, 1936, 2209, 2500, 2809, 3136, 3481, 3844, 4225, 4624, 5041, 5476, 5929, 6400, 6889, 7396, 7921, 8464, 9025, 9604, 10201, 10816, 11449, 12100, 12769, 13456, 14161, 14884, 15625, 16384

Offset

-1,2

Comments

If Y is a fixed 2-subset of a (3n+1)-set X then a(n-1) is the number of 3-subsets of X intersecting Y. - Milan Janjic, Oct 21 2007

The digit root of the sequence, i.e., A010888(a(n)) for n>=0, is a repeating pattern of {4,7,1}, cf. A100402. - Ram Shankar, Apr 14 2015

With a different offset, partial sums of A298035. - N. J. A. Sloane, Jan 22 2018

Links

Vincenzo Librandi, Table of n, a(n) for n = -1..3000

Milan Janjic, Two Enumerative Functions

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

Formula

a(n) = A016958(n)/4. - Zerinvary Lajos, Jun 30 2009

From Wesley Ivan Hurt, Apr 14 2015: (Start)

G.f.: (4+13*x+x^2)/(1-x)^3.

a(n) = 3*a(n-1)-3*a(n-2)+a(n-3). (End)

a(n) = a(n-1)+3*(6*n+1). - Miquel Cerda, Oct 25 2016

a(n) = A016766(n+1)-A016969(n). - Miquel Cerda, Oct 26 2016

Sum_{n>=0} 1/a(n) = A294967. - Amiram Eldar, Nov 12 2020

Maple

A016790:=n->(3*n+2)^2: seq(A016790(n), n=0..50); # Wesley Ivan Hurt, Apr 14 2015

Mathematica

(3 Range[0, 50] + 2)^2 (* Wesley Ivan Hurt, Apr 14 2015 *)

Prog

(Magma) [(3*n+2)^2: n in [0..50]]; // Vincenzo Librandi, May 06 2011
(PARI) vector(50, n, n--; (3*n+2)^2) \\ Derek Orr, Apr 14 2015

Crossrefs

Cf. A016957, A016958, A294967, A298035.

Sequence in context: A337173 A135784 A131069 * A065733 A368245 A212893

Adjacent sequences: A016787 A016788 A016789 * A016791 A016792 A016793

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

Notation in formula cleaned up by R. J. Mathar, Aug 05 2010

Added a(-1)=1 and fixed b-file. Note: this sequence should really be changed to a(n) = (3n-1)^2 and have offset 0. - N. J. A. Sloane, Jan 22 2018

Status

approved