This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A092498 #55 Apr 05 2023 18:51:02
%S A092498 1,4,11,23,41,67,102,147,204,274,358,458,575,710,865,1041,1239,1461,
%T A092498 1708,1981,2282,2612,2972,3364,3789,4248,4743,5275,5845,6455,7106,
%U A092498 7799,8536,9318,10146,11022,11947,12922,13949,15029,16163,17353,18600,19905,21270
%N A092498 Expansion of g.f. (1 + x + 2*x^2)/((1 - x)^3*(1 - x^3)).
%C A092498 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)).
%C A092498 From Philippe LALLOUET (philip.lallouet(AT)wanadoo.fr), Sep 24 2007: (Start)
%C A092498 Also arises when a pyramid is built row by row with squares of size 1.
%C A092498 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.
%C A092498 ..........................__
%C A092498 ..........__...........__|__|__..
%C A092498 .__....__|__|__.....__|__|__|__|__
%C A092498 |__|..|__|__|__|...|__|__|__|__|__|
%C A092498 The table below gives the number of squares by size, and the total number of squares (i.e., a(n)), for each row.
%C A092498 +-----------------------+
%C A092498 |size size size size |
%C A092498 n | 1 2 3 4 | a(n)
%C A092498 --+-----------------------+-----
%C A092498 1 | .1....................|....1
%C A092498 2 | .4....................|....4
%C A092498 3 | .9....2...............|...11
%C A092498 4 | 16....6....1..........|...23
%C A092498 5 | 25...12....4..........|...41
%C A092498 6 | 36...20....9....2.....|...67
%C A092498 (End)
%H A092498 Vincenzo Librandi, <a href="/A092498/b092498.txt">Table of n, a(n) for n = 0..1000</a>
%H A092498 G. Nebe, E. M. Rains, and N. J. A. Sloane, <a href="http://neilsloane.com/doc/cliff2.html">Self-Dual Codes and Invariant Theory</a>, Springer, Berlin, 2006.
%H A092498 <a href="/index/Mo#Molien">Index entries for Molien series</a>
%H A092498 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,2,-3,3,-1).
%F A092498 a(n) = (4*n^3+21*n^2+35*n+18-6*floor((n+2)/3))/18. - _Luce ETIENNE_, Apr 18 2014
%F A092498 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
%F A092498 E.g.f.: exp(-x/2)*(3*exp(3*x/2)*(2 + x)*(8 + 25*x + 4*x^2) + 6*cos(sqrt(3)*x/2) - 2*sqrt(3)*sin(sqrt(3)*x/2))/54. - _Stefano Spezia_, Apr 05 2023
%p A092498 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
%t A092498 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 *)
%t A092498 CoefficientList[Series[(1 + x + 2 x^2)/((1 - x)^3 (1 -x^3)), {x, 0, 40 }], x] (* _Vincenzo Librandi_, Apr 20 2014 *)
%t A092498 LinearRecurrence[{3,-3,2,-3,3,-1},{1,4,11,23,41,67},50] (* _Harvey P. Dale_, Jul 08 2017 *)
%Y A092498 Cf. A014126.
%Y A092498 Cf. A000969 (first differences). - _R. J. Mathar_, Jan 05 2009
%K A092498 nonn,easy
%O A092498 0,2
%A A092498 _N. J. A. Sloane_, Apr 05 2004
%E A092498 Edited by _N. J. A. Sloane_, May 15 2014