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 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 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

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