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A224149 Number of 5 X n 0..1 arrays with rows and antidiagonals unimodal and columns nondecreasing. 1

%I

%S 6,36,155,526,1509,3827,8838,18969,38392,74053,137204,245636,426869,

%T 722624,1194983,1934737,3072530,4793530,7356497,11118274,16564901,

%U 24350745,35347252,50703161,71918276,100933171,140237506,192999960

%N Number of 5 X n 0..1 arrays with rows and antidiagonals unimodal and columns nondecreasing.

%C Row 5 of A224146.

%H R. H. Hardin, <a href="/A224149/b224149.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (1/3628800)*n^10 + (1/241920)*n^9 + (11/120960)*n^8 + (59/40320)*n^7 + (3853/172800)*n^6 + (181/1280)*n^5 + (100381/181440)*n^4 + (76319/60480)*n^3 + (24247/12600)*n^2 + (23/21)*n + 1.

%F Conjectures from _Colin Barker_, Aug 28 2018: (Start)

%F G.f.: x*(6 - 30*x + 89*x^2 - 189*x^3 + 288*x^4 - 309*x^5 + 236*x^6 - 127*x^7 + 46*x^8 - 10*x^9 + x^10) / (1 - x)^11.

%F a(n) = 11*a(n-1) - 55*a(n-2) + 165*a(n-3) - 330*a(n-4) + 462*a(n-5) - 462*a(n-6) + 330*a(n-7) - 165*a(n-8) + 55*a(n-9) - 11*a(n-10) + a(n-11) for n>11.

%F (End)

%e Some solutions for n=3:

%e ..0..1..0....0..0..0....0..1..0....0..0..0....0..0..0....0..0..1....0..0..0

%e ..1..1..0....0..0..0....0..1..0....0..1..0....0..1..0....0..0..1....1..0..0

%e ..1..1..1....0..1..0....0..1..0....0..1..1....1..1..0....0..1..1....1..1..0

%e ..1..1..1....0..1..0....0..1..0....1..1..1....1..1..0....0..1..1....1..1..0

%e ..1..1..1....1..1..1....1..1..1....1..1..1....1..1..1....0..1..1....1..1..1

%Y Cf. A224146.

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 31 2013

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Last modified June 27 22:27 EDT 2022. Contains 354899 sequences. (Running on oeis4.)