login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A092498 G.f.: (1+x+2x^2)/((1-x)^3*(1-x^3)). 8
1, 4, 11, 23, 41, 67, 102, 147, 204, 274, 358, 458, 575, 710, 865, 1041, 1239, 1461, 1708, 1981, 2282, 2612, 2972, 3364, 3789, 4248, 4743, 5275, 5845, 6455, 7106, 7799, 8536, 9318, 10146, 11022, 11947, 12922, 13949, 15029, 16163, 17353, 18600, 19905, 21270 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Arises from the Molien series for 4-dimensional group of structure S_3 X C_2 and order 12, which preserves the complete weight enumerators of even trace-Hermitian self-dual additive codes over GF(4). The Molien series is (1 + x^2 + 2*x^4)/((1 - x^2)^3 *(1 - x^6)).

From Philippe LALLOUET (philip.lallouet(AT)wanadoo.fr), Sep 24 2007: (Start)

Also arises when a pyramid is built row by row with squares of size 1.

At the first step, we put a single square on row 1. At the second, we put a square above the first one, on row 2, and a square on each of its sides on row 1. At each following step, we begin a new row with one square and add a square at each end of each of the previous rows. The term a(n) of the sequence is the total number of squares of any size which can be seen in the entire triangular array.

..........................__

..........__...........__|__|__..

.__....__|__|__.....__|__|__|__|__

|__|..|__|__|__|...|__|__|__|__|__|

The table below gives the number of squares by size, and the total number of squares (i.e., a(n)), for each row.

  +-----------------------+

  |size size size size    |

n |  1    2    3    4     | a(n)

--+-----------------------+-----

1 | .1....................|....1

2 | .4....................|....4

3 | .9....2...............|...11

4 | 16....6....1..........|...23

5 | 25...12....4..........|...41

6 | 36...20....9....2.....|...67

(End)

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

G. Nebe, E. M. Rains and N. J. A. Sloane, Self-Dual Codes and Invariant Theory, Springer, Berlin, 2006.

Index entries for Molien series

Index entries for linear recurrences with constant coefficients, signature (3,-3,2,-3,3,-1).

FORMULA

a(n) = (4*n^3+21*n^2+35*n+18-6*floor((n+2)/3))/18. - Luce ETIENNE, Apr 18 2014

a(n) = Sum_{j=0..floor(2*n/3)} ((4*n+5-6*j-(-1)^j)/4)*((4*n+3-6*j+(-1)^j)/4). - Luce ETIENNE, Oct 28 2014

MAPLE

A092498:=n->(4*n^3+21*n^2+35*n+18-6*floor((n+2)/3))/18; seq(A092498(n), n=0..50); # Wesley Ivan Hurt, Apr 19 2014

MATHEMATICA

Table[(4*n^3 + 21*n^2 + 35*n + 18 - 6*Floor[(n + 2)/3])/18, {n, 0, 50}] (* Wesley Ivan Hurt, Apr 19 2014 *)

CoefficientList[Series[(1 + x + 2 x^2)/((1 - x)^3 (1 -x^3)), {x, 0, 40 }], x] (* Vincenzo Librandi, Apr 20 2014 *)

LinearRecurrence[{3, -3, 2, -3, 3, -1}, {1, 4, 11, 23, 41, 67}, 50] (* Harvey P. Dale, Jul 08 2017 *)

CROSSREFS

Cf. A014126.

Cf. A000969 (first differences). - R. J. Mathar, Jan 05 2009

Sequence in context: A298023 A027378 A131177 * A301165 A019298 A237586

Adjacent sequences:  A092495 A092496 A092497 * A092499 A092500 A092501

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Apr 05 2004

EXTENSIONS

Edited by N. J. A. Sloane, May 15 2014

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 31 05:09 EDT 2021. Contains 346367 sequences. (Running on oeis4.)