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 A175197 Array A(k,n) of the number of points of the A_k lattice with maximum infinity norm n, read by antidiagonals. 0
 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, 1, 392, 1610, 1070, 258, 30, 2, 0, 1, 1106, 7742, 7580, 2500, 402, 36, 2, 0, 1, 3138, 37058, 52556, 23330, 4850, 578, 42, 2, 0, 1, 8952, 177186, 360402, 212436, 56252, 8350, 786 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS 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: .1,....1,......1,.......1,........1,........1,.........1,.........1,.........1 .1,....3,......5,.......7,........9,.......11,........13,........15,........17 .1,....7,.....19,......37,.......61,.......91,.......127,.......169,.......217 .1,...19,.....85,.....231,......489,......891,......1469,......2255,......3281 .1,...51,....381,....1451,.....3951,.....8801,.....17151,.....30381,.....50101 .1,..141,...1751,....9331,....32661,....88913,....204763,....418503,....782153 .1,..393,...8135,...60691,...273127,...908755,...2473325,...5832765,..12354469 .1,.1107,..38165,..398567,..2306025,..9377467,..30162301,..82073295,.197018321 .1,.3139,.180325,.2636263,.19610233,.97464799,.370487485,1163205475,3164588407 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. LINKS Table of n, a(n) for n=0..62. R. J. Mathar, Point counts of D_k and some A_k and E_K integer.., arXiv:1002.3844 [math .GT], variable A_k^s(n). EXAMPLE A(k,n) starts in row k=0, column n=0 as: 1,....0,......0,.......0,........0,........0,.........0,.........0,.........0 1,....2,......2,.......2,........2,........2,.........2,.........2,.........2 1,....6,.....12,......18,.......24,.......30,........36,........42,........48 1,...18,.....66,.....146,......258,......402,.......578,.......786,......1026 1,...50,....330,....1070,.....2500,.....4850,......8350,.....13230,.....19720 1,..140,...1610,....7580,....23330,....56252,....115850,....213740,....363650 1,..392,...7742,...52556,...212436,...635628,...1564570,...3359440,...6521704 1,.1106,..37058,..360402,..1907458,..7071442,..20784834,..51910994,.114945026 1,.3138,.177186,.2455938,.16973970,.77854566,.273022686,.792717990,2001382932 CROSSREFS Cf. A008458 (row k=2), A010006 (row k=3), A110907. Sequence in context: A276436 A161121 A021500 * A367795 A343825 A339031 Adjacent sequences: A175194 A175195 A175196 * A175198 A175199 A175200 KEYWORD easy,nonn,tabl AUTHOR R. J. Mathar, Mar 02 2010 STATUS approved

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Last modified July 12 21:16 EDT 2024. Contains 374257 sequences. (Running on oeis4.)