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 A105373 Square array by antidiagonals of number of straight lines with n points in a k-dimensional hypercube of with n points on each edge. 1
 1, 1, 1, 1, 6, 1, 1, 28, 8, 1, 1, 120, 49, 10, 1, 1, 496, 272, 76, 12, 1, 1, 2016, 1441, 520, 109, 14, 1, 1, 8128, 7448, 3376, 888, 148, 16, 1, 1, 32640, 37969, 21280, 6841, 1400, 193, 18, 1, 1, 130816, 192032, 131776, 51012, 12496, 2080, 244, 20, 1, 1, 523776 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 LINKS FORMULA T(1, k)=1. For n>1: T(n, k) = ((n+2)^k-n^k)/2 = (n+2)*T(n, k-1)+n^(k-1) = A102728(k, n+1). EXAMPLE Rows start:   1,  1,   1,   1,    1,     1, ...;   1,  6,  28, 120,  496,  2016, ...;   1,  8,  49, 272, 1441,  7448, ...;   1, 10,  76, 520, 3376, 21280, ...;   1, 12, 109, 888, 6841, 51012, ...;   etc. T(5,3)=109 because in a 5 X 5 X 5 cube there are 25 columns, 25 linear rows in one direction, 25 linear rows in another direction, 5 short diagonals in each of 6 directions and 4 long diagonals; and 3*25 + 6*5 + 4 = 109. CROSSREFS See A102728. Rows essentially include A000012, A006516, A005059, A016149 or A081199, A016161 or A081200, A016170 or A081201, A016178 or A081202 etc. Columns essentially include A000012, A005843, A056107, A105373. Sequence in context: A141688 A166960 A155908 * A201461 A265603 A174186 Adjacent sequences:  A105370 A105371 A105372 * A105374 A105375 A105376 KEYWORD nonn,tabl AUTHOR Henry Bottomley, Apr 02 2005 STATUS approved

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