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%I #25 Mar 13 2023 06:51:51
%S 0,10,108,1126,11506,116166,1168586,11749134,118127408,1187692422,
%T 11941503498,120064335342,1207171430452,12137349489598,
%U 122033415224922,1226969238084836,12336404001299200,124034783402890620
%N Number of nonzero 4 X n binary arrays with all 1's connected.
%C Old name was "Number of 4 X n checkerboards in which the set of red squares is edge connected".
%C The number of connected (non-null) induced subgraphs in the grid graph P_4 X P_n. - _Andrew Howroyd_, May 20 2017
%H Andrew Howroyd, <a href="/A059524/b059524.txt">Table of n, a(n) for n = 0..200</a>
%F Empirical: checked against 200 terms b-file with linear recurrence with signature (17, -90, 230, -272, -75, 623, -632, 65, 255, -198, 162, -96, 11, 1). - _Jean-François Alcover_, Oct 11 2017
%F Empirical g.f.: 2*x*(1 + x)*(5 - 36*x + 131*x^2 - 239*x^3 + 131*x^4 + 94*x^5 - 157*x^6 + 61*x^7 - 73*x^8 + 18*x^9 + x^10) / ((1 - x)^2*(1 - 15*x + 59*x^2 - 97*x^3 + 19*x^4 + 210*x^5 - 222*x^6 - 22*x^7 + 113*x^8 - 7*x^9 + 71*x^10 - 13*x^11 - x^12)). - _Colin Barker_, Oct 11 2017
%e a(1) = 10 because there are 4 positions to place a single 1, 3 ways to place a pair of adjacent 1's, 2 ways to place a triple of connected 1's, and 1 way for the all-1's array: 4+3+2+1=10. - _R. J. Mathar_, Mar 13 2023
%Y Row 4 of A287151.
%Y Cf. A059020, A059021.
%K nonn
%O 0,2
%A _David Radcliffe_, Jan 21 2001
%E Clearer name from _R. H. Hardin_, Jul 06 2009
%E a(16) corrected by _Andrew Howroyd_, May 20 2017