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 A267243 Number of n X 6 binary arrays with row sums nondecreasing and columns lexicographically nondecreasing. 1
 7, 50, 475, 6292, 107015, 2093467, 43555569, 924051709, 19614050515, 413556580944, 8645774602327, 179276181587698, 3691120876565687, 75550095426967737, 1538986699132717645, 31229753343696948035 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Column 6 of A267245. LINKS R. H. Hardin, Table of n, a(n) for n = 1..210 Robert Israel, Maple-assisted proof of empirical recurrence Index entries for linear recurrences with constant coefficients, signature (114, -5915, 186008, -3982785, 61835542, -723657627, 6549515604, -46652032035, 264676225246, -1205477853945, 4427867737616, -13139368875011, 31468929403866, -60602488003009, 93197329064964, -113220771193368, 106920682204032, -76630180181904, 40173465734208, -14497964755200, 3213273369600, -329204736000). FORMULA Empirical: a(n) = 114*a(n-1) - 5915*a(n-2) + 186008*a(n-3) - 3982785*a(n-4) + 61835542*a(n-5) - 723657627*a(n-6) + 6549515604*a(n-7) - 46652032035*a(n-8) + 264676225246*a(n-9) - 1205477853945*a(n-10) + 4427867737616*a(n-11) - 13139368875011*a(n-12) + 31468929403866*a(n-13) - 60602488003009*a(n-14) + 93197329064964*a(n-15) - 113220771193368*a(n-16) + 106920682204032*a(n-17) - 76630180181904*a(n-18) + 40173465734208*a(n-19) - 14497964755200*a(n-20) + 3213273369600*a(n-21) - 329204736000*a(n-22). Empirical formula verified (see link). - Robert Israel, Sep 08 2019 EXAMPLE Some solutions for n=4: 0 0 0 0 1 1 0 0 0 0 1 1 0 0 0 0 1 1 0 0 0 1 1 1 0 0 0 1 0 1 0 0 1 1 0 0 0 0 1 1 0 0 0 1 1 0 0 1 0 1 1 1 1 0 0 0 0 1 1 1 0 1 0 0 0 1 1 1 1 1 1 0 0 0 1 1 1 1 0 1 0 1 0 1 1 1 0 1 0 1 1 0 1 1 1 1 MAPLE S[2]:= [[0, 0, 0], [0, 0, 1], [0, 1, 1], [1, 0, 1], [1, 1, 0], [1, 1, 1]]: for i from 3 to 6 do S[i]:= map(proc(t) [op(t[1..i-1]), t[i-1], op(t[i..-1]), 0], [op(t[1..i-1]), t[i-1], op(t[i..-1]), 1], [op(t[1..i-1]), 1-t[i-1], op(t[i..-1]), 1] end proc, S[i-1]) od: states:= S[6]: T:= Matrix(486, 486, proc(i, j) local k; if add(states[j, k]-states[i, k], k=1..6) > 0 then return 0 fi; for k from 7 to 11 do if states[j, k]>states[i, k] then return 0 fi od; for k from 1 to 5 do if states[i, k]>=states[i, k+1] and states[j, k+6]<>states[i, k+6] then return 0 fi od; 1 end proc): E:= Vector(486): E[1]:= 1: U[0]:= Vector[row](486, 1): for k from 1 to 25 do U[k]:= U[k-1].T od: seq(U[j] . E, j=1..25); # Robert Israel, Sep 08 2019 CROSSREFS Cf. A267245. Sequence in context: A355171 A266432 A369473 * A197570 A319884 A204463 Adjacent sequences: A267240 A267241 A267242 * A267244 A267245 A267246 KEYWORD nonn AUTHOR R. H. Hardin, Jan 12 2016 STATUS approved

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Last modified April 15 12:37 EDT 2024. Contains 371687 sequences. (Running on oeis4.)