cp's OEIS Frontend

A105373 Square array by antidiagonals of number of straight lines with n points in a k-dimensional hypercube with n points on each edge.

%I A105373 #15 May 20 2025 08:26:27
%S A105373 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,
%T A105373 109,14,1,1,8128,7448,3376,888,148,16,1,1,32640,37969,21280,6841,1400,
%U A105373 193,18,1,1,130816,192032,131776,51012,12496,2080,244,20,1,1,523776
%N A105373 Square array by antidiagonals of number of straight lines with n points in a k-dimensional hypercube with n points on each edge.
%F A105373 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).
%e A105373 Rows start:
%e A105373   1,  1,   1,   1,    1,     1, ...;
%e A105373   1,  6,  28, 120,  496,  2016, ...;
%e A105373   1,  8,  49, 272, 1441,  7448, ...;
%e A105373   1, 10,  76, 520, 3376, 21280, ...;
%e A105373   1, 12, 109, 888, 6841, 51012, ...;
%e A105373   etc.
%e A105373 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.
%Y A105373 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.
%K A105373 nonn,tabl
%O A105373 1,5
%A A105373 _Henry Bottomley_, Apr 02 2005