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A227259
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Number of n X 2 0,1 arrays indicating 2 X 2 subblocks of some larger (n+1) X 3 binary array having a sum of two or less, with rows and columns of the latter in lexicographically nondecreasing order.
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2
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3, 9, 23, 50, 96, 168, 274, 423, 625, 891, 1233, 1664, 2198, 2850, 3636, 4573, 5679, 6973, 8475, 10206, 12188, 14444, 16998, 19875, 23101, 26703, 30709, 35148, 40050, 45446, 51368, 57849, 64923, 72625, 80991, 90058, 99864, 110448, 121850, 134111
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OFFSET
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1,1
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COMMENTS
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Conjecture: a(n) is also the number of length n strings of {0,1,2} with digit sum <= 4 (holds if the empirical formula holds). - Daniel T. Martin, May 24 2023
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LINKS
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FORMULA
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Empirical: a(n) = (1/24)*n^4 + (5/12)*n^3 + (11/24)*n^2 + (13/12)*n + 1.
G.f.: x*(3 - 6*x + 8*x^2 - 5*x^3 + x^4) / (1 - x)^5. (Conjecture from Colin Barker, Sep 07 2018)
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EXAMPLE
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Some solutions for n=4:
1 0 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 0 1 1
1 1 1 0 1 0 1 1 1 1 1 1 1 1 0 1 0 0 1 1
1 1 0 0 0 1 1 1 0 1 0 1 1 1 0 0 0 0 0 0
0 1 0 0 0 1 1 0 0 1 0 1 0 0 0 0 0 0 0 0
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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