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%I #4 Dec 10 2016 17:31:42
%S 1,1,0,1,2,0,1,6,2,0,1,18,12,2,0,1,50,66,18,2,0,1,140,330,146,24,2,0,
%T 1,392,1610,1070,258,30,2,0,1,1106,7742,7580,2500,402,36,2,0,1,3138,
%U 37058,52556,23330,4850,578,42,2,0,1,8952,177186,360402,212436,56252,8350,786
%N Array A(k,n) of the number of points of the A_k lattice with maximum infinity norm n, read by antidiagonals.
%C The values are computed starting with an auxiliary array which places the centered trinomial numbers A002426, the centered pentanomial numbers A005191, the centered 7-nomial numbers A025012 etc. into separate columns:
%C .1,....1,......1,.......1,........1,........1,.........1,.........1,.........1
%C .1,....3,......5,.......7,........9,.......11,........13,........15,........17
%C .1,....7,.....19,......37,.......61,.......91,.......127,.......169,.......217
%C .1,...19,.....85,.....231,......489,......891,......1469,......2255,......3281
%C .1,...51,....381,....1451,.....3951,.....8801,.....17151,.....30381,.....50101
%C .1,..141,...1751,....9331,....32661,....88913,....204763,....418503,....782153
%C .1,..393,...8135,...60691,...273127,...908755,...2473325,...5832765,..12354469
%C .1,.1107,..38165,..398567,..2306025,..9377467,..30162301,..82073295,.197018321
%C .1,.3139,.180325,.2636263,.19610233,.97464799,.370487485,1163205475,3164588407
%C This is a subarray of A077042. Rows are A005408, A003215, A063496, A083669 (see A077044) etc. The array A(k,n) is the first differences along each row of this auxiliary array.
%H R. J. Mathar, <a href="http://arxiv.org/abs/1002.3844">Point counts of D_k and some A_k and E_K integer..</a>, arXiv:1002.3844 [math .GT], variable A_k^s(n).
%e A(k,n) starts in row k=0, column n=0 as:
%e 1,....0,......0,.......0,........0,........0,.........0,.........0,.........0
%e 1,....2,......2,.......2,........2,........2,.........2,.........2,.........2
%e 1,....6,.....12,......18,.......24,.......30,........36,........42,........48
%e 1,...18,.....66,.....146,......258,......402,.......578,.......786,......1026
%e 1,...50,....330,....1070,.....2500,.....4850,......8350,.....13230,.....19720
%e 1,..140,...1610,....7580,....23330,....56252,....115850,....213740,....363650
%e 1,..392,...7742,...52556,...212436,...635628,...1564570,...3359440,...6521704
%e 1,.1106,..37058,..360402,..1907458,..7071442,..20784834,..51910994,.114945026
%e 1,.3138,.177186,.2455938,.16973970,.77854566,.273022686,.792717990,2001382932
%Y Cf. A008458 (row k=2), A010006 (row k=3), A110907.
%K easy,nonn,tabl
%O 0,5
%A _R. J. Mathar_, Mar 02 2010
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