proposed

approved

editing

proposed

Number of 6Xn 6 X n 0..1 arrays with diagonals and antidiagonals unimodal and rows nondecreasing.

Row 6 of A223949.

Empirical: a(n) = (2/45)*n^6 + (67/36)*n^4 + 8*n^3 + (7757/180)*n^2 + 138*n + 1326 for n>4.

Conjectures from Colin Barker, Aug 24 2018: (Start)

G.f.: x*(64 + 281*x - 1735*x^2 + 2546*x^3 - 335*x^4 - 1862*x^5 + 787*x^6 + 767*x^7 - 426*x^8 - 148*x^9 + 93*x^10) / (1 - x)^7.

a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>11.

(End)

Some solutions for n=3:

Cf. A223949.

R. H. Hardin , Mar 29 2013

approved

editing

editing

approved

R. H. Hardin, <a href="/A223953/b223953.txt">Table of n, a(n) for n = 1..210</a>

allocated for R. H. Hardin

Number of 6Xn 0..1 arrays with diagonals and antidiagonals unimodal and rows nondecreasing

64, 729, 2024, 3645, 5951, 9919, 16845, 28558, 47721, 78071, 124691, 194314, 295659, 439799, 640561, 914958, 1283653, 1771455, 2407847, 3227546, 4271095, 5585487, 7224821, 9250990, 11734401, 14754727, 18401691, 22775882, 27989603, 34167751

1,1

Row 6 of A223949

Empirical: a(n) = (2/45)*n^6 + (67/36)*n^4 + 8*n^3 + (7757/180)*n^2 + 138*n + 1326 for n>4

Some solutions for n=3

..0..1..1....0..0..0....1..1..1....1..1..1....0..0..1....1..1..1....0..0..1

..0..0..0....0..0..0....0..1..1....0..1..1....0..1..1....0..0..1....0..0..1

..0..0..0....0..0..1....1..1..1....0..0..0....0..0..0....0..0..0....0..0..0

..0..0..0....0..0..1....1..1..1....0..0..0....0..0..0....0..0..1....0..1..1

..0..1..1....0..1..1....0..0..1....0..1..1....0..0..1....0..0..1....1..1..1

..0..0..0....0..0..1....0..0..0....0..0..1....1..1..1....0..0..1....0..0..0

allocated

nonn

R. H. Hardin Mar 29 2013

approved

editing

allocated for R. H. Hardin

allocated

approved