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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
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
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 * A376983 A367795 A343825
KEYWORD
easy,nonn,tabl
AUTHOR
R. J. Mathar, Mar 02 2010
STATUS
approved