A140676 a(n) = n*(3*n + 4).

0, 7, 20, 39, 64, 95, 132, 175, 224, 279, 340, 407, 480, 559, 644, 735, 832, 935, 1044, 1159, 1280, 1407, 1540, 1679, 1824, 1975, 2132, 2295, 2464, 2639, 2820, 3007, 3200, 3399, 3604, 3815, 4032, 4255, 4484, 4719, 4960, 5207, 5460, 5719, 5984, 6255, 6532, 6815

Offset: 0

Author

Omar E. Pol, May 22 2008

Keywords

• nonn
• easy

Comments

The number of peers of a cell of an n^2 X n^2 sudoku is a(n-1). - Neven Sajko, Apr 20 2016

First differences are in A016921. - Wesley Ivan Hurt, Apr 21 2016

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. A000567, A016921, A033428, A045944, A067707, A067725, A140677, A140678, A140679, A140680, A140681, A140689.

Programs

Magma

[n*(3*n+4) : n in [0..80]]; // Wesley Ivan Hurt, Apr 21 2016

Maple

A140676:=n->n*(3*n+4): seq(A140676(n), n=0..100); # Wesley Ivan Hurt, Apr 21 2016

Mathematica

Table[n (3 n + 4), {n, 0, 50}] (* or *) LinearRecurrence[{3, -3, 1}, {0, 7, 20}, 50] (* Harvey P. Dale, May 04 2013 *)

PARI

a(n)=n*(3*n+4) \\ Charles R Greathouse IV, Oct 07 2015

Formula

a(n) = 3*n^2 + 4*n.

a(n) = 6*n + a(n-1) + 1 for n>0, a(0)=0. - Vincenzo Librandi, Aug 03 2010

O.g.f.: x*(7 - x)/(1 - x)^3. - Arkadiusz Wesolowski, Dec 24 2011

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>2. - Harvey P. Dale, May 04 2013

E.g.f.: x*(7 + 3*x)*exp(x). - Ilya Gutkovskiy, Apr 20 2016

a(n) = A000567(n+1) - 1. - Neven Sajko, Apr 20 2016

From Amiram Eldar, Feb 26 2022: (Start)

Sum_{n>=1} 1/a(n) = 15/16 - Pi/(8*sqrt(3)) - 3*log(3)/8.

Sum_{n>=1} (-1)^(n+1)/a(n) = 9/16 - Pi/(4*sqrt(3)). (End)