cp's OEIS Frontend

A068745 Number of potential flows in 4 X 4 array with integer velocities in -n..n, i.e., number of 4 X 4 arrays with adjacent elements differing by no more than n, counting arrays differing by a constant only once.

%I A068745 #11 Jul 30 2017 22:25:08
%S A068745 1,690437,1133641543,164185416899,6913624013061,138190481342321,
%T A068745 1678843050246451,14285299502131463,93044501704039945,
%U A068745 492225938556374973,2204710243834695807,8617480381892283531
%N A068745 Number of potential flows in 4 X 4 array with integer velocities in -n..n, i.e., number of 4 X 4 arrays with adjacent elements differing by no more than n, counting arrays differing by a constant only once.
%F A068745 Let y = 2*n - 1; it appears that a(n) = y*(2623243666*y^14 + 9598591135*y^12 + 17180805187*y^10 + 20342655905*y^8 + 17636121503*y^6 + 10907793260*y^4 + 3135618144*y^2 + 304819200)/81729648000. - _R. H. Hardin_, Jan 01 2007
%Y A068745 2 X 2 A063496, 3 X 3 A068744, 5 X 5 A068746, 6 X 6 A068747, by velocity limit 1..14 A068748-A068761, solenoidal flows A068722-A068738.
%Y A068745 Cf. 4 X 4 this sequence (degree 4*4-1) with factor 2n-1 ; 3 X 3 A068744 (degree 3*3-1) with factor (2n-1)^2 ; 2 X 2 A063496 (degree 2*2-1) with factor 2n-1.
%K A068745 nonn
%O A068745 0,2
%A A068745 _R. H. Hardin_, Feb 27 2002