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A059524
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Number of nonzero 4 X n binary arrays with all 1's connected.
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4
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0, 10, 108, 1126, 11506, 116166, 1168586, 11749134, 118127408, 1187692422, 11941503498, 120064335342, 1207171430452, 12137349489598, 122033415224922, 1226969238084836, 12336404001299200, 124034783402890620
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OFFSET
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0,2
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COMMENTS
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Old name was "Number of 4 X n checkerboards in which the set of red squares is edge connected".
The number of connected (non-null) induced subgraphs in the grid graph P_4 X P_n. - Andrew Howroyd, May 20 2017
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LINKS
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FORMULA
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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
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
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EXAMPLE
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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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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