

A059524


Number of nonzero 4 X n binary arrays with all 1's connected.


4



0, 10, 108, 1126, 11506, 116166, 1168586, 11749134, 118127408, 1187692422, 11941503498, 120064335342, 1207171430452, 12137349489598, 122033415224922, 1226969238084836, 12336404001299200, 124034783402890620
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OFFSET

0,2


COMMENTS

Old name was "Number of 4 X n checkerboards in which the set of red squares is edge connected".
The number of connected (nonnull) induced subgraphs in the grid graph P_4 X P_n.  Andrew Howroyd, May 20 2017


LINKS



FORMULA

Empirical: checked against 200 terms bfile with linear recurrence with signature (17, 90, 230, 272, 75, 623, 632, 65, 255, 198, 162, 96, 11, 1).  JeanFrançois 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


EXAMPLE

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 all1's array: 4+3+2+1=10.  R. J. Mathar, Mar 13 2023


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



