A250729 -id:A250729 - cp's OEIS frontend

A250733 Number of (4+1) X (n+1) 0..1 arrays with nondecreasing x(i,j)+x(i,j-1) in the i direction and nondecreasing min(x(i,j),x(i-1,j)) in the j direction.

58, 144, 365, 885, 2092, 4889, 11377, 26419, 61330, 142336, 330417, 767047, 1781019, 4135537, 9603827, 22303104, 51797791, 120298572, 279397140, 648909915, 1507137312, 3500429630, 8130041844, 18882699707, 43856786967, 101861340070

Offset: 1

R. H. Hardin, Nov 27 2014

nonn

			Some solutions for n=4:
..0..0..0..0..0....0..0..0..0..1....0..0..0..0..0....0..0..0..0..0
..0..0..0..0..0....0..0..0..0..1....0..0..0..0..0....0..0..0..0..0
..0..0..0..0..0....0..0..0..0..1....0..0..0..0..1....0..0..0..1..1
..1..0..0..0..1....1..0..1..1..1....0..0..0..1..0....0..0..1..1..1
..0..1..1..1..0....0..1..1..1..1....0..0..1..0..1....0..1..1..1..1

R. H. Hardin, Table of n, a(n) for n = 1..210

Row 4 of A250729.

Empirical: a(n) = 4*a(n-1) - a(n-2) - 13*a(n-3) + 15*a(n-4) + 3*a(n-5) - 11*a(n-6) + 4*a(n-7) for n>9.

Empirical g.f.: x*(58 - 88*x - 153*x^2 + 323*x^3 - 81*x^4 - 183*x^5 + 149*x^6 - 22*x^7 - 8*x^8) / ((1 - x)^2*(1 - 2*x - 4*x^2 + 7*x^3 + 3*x^4 - 4*x^5)). - Colin Barker, Nov 16 2018

A250734 Number of (5+1) X (n+1) 0..1 arrays with nondecreasing x(i,j)+x(i,j-1) in the i direction and nondecreasing min(x(i,j),x(i-1,j)) in the j direction.

Original entry on oeis.org

99, 230, 600, 1500, 3605, 8514, 19887, 46315, 107565, 249853, 579962, 1346953, 3127694, 7265717, 16877299, 39213972, 91109305, 211714501, 491957956, 1143254321, 2656749170, 6174181500, 14348397804, 33345661179, 77494714919

Offset: 1

R. H. Hardin, Nov 27 2014

nonn

			Some solutions for n=4:
..0..0..0..0..0....0..0..0..0..0....0..0..0..0..0....1..0..0..0..0
..0..0..0..0..1....0..0..0..0..1....0..0..0..0..0....0..1..0..0..0
..0..0..0..0..1....1..0..0..1..1....0..0..0..1..0....1..0..1..0..0
..0..0..0..0..1....0..1..1..1..1....1..0..1..0..1....0..1..0..1..1
..0..0..0..1..1....0..1..1..1..1....0..1..0..1..1....1..0..1..1..1
..0..1..0..1..1....0..1..1..1..1....1..0..1..1..1....0..1..1..1..1

R. H. Hardin, Table of n, a(n) for n = 1..210

Row 5 of A250729.

Empirical: a(n) = 4*a(n-1) - 17*a(n-3) + 17*a(n-4) + 12*a(n-5) - 23*a(n-6) + 6*a(n-7) + 3*a(n-8) - a(n-9) for n>12.

Empirical g.f.: x*(99 - 166*x - 320*x^2 + 783*x^3 - 168*x^4 - 804*x^5 + 648*x^6 + 48*x^7 - 119*x^8 - 17*x^9 + 3*x^10 + 3*x^11) / ((1 - x)^3*(1 - x - 6*x^2 + 3*x^3 + 9*x^4 - x^6)). - Colin Barker, Nov 16 2018

A250735 Number of (6+1)X(n+1) 0..1 arrays with nondecreasing x(i,j)+x(i,j-1) in the i direction and nondecreasing min(x(i,j),x(i-1,j)) in the j direction.

Original entry on oeis.org

166, 350, 942, 2434, 6016, 14437, 34069, 79704, 185684, 431691, 1002869, 2329047, 5409245, 12563824, 29186388, 67808124, 157558290, 366127187, 850864580, 1977462106, 4595987342, 10682199696, 24828823703, 57710916319, 134142923156

Offset: 1

R. H. Hardin, Nov 27 2014

nonn

Row 6 of A250729

			Some solutions for n=4
..0..0..0..0..0....0..0..0..0..1....0..0..0..0..1....0..0..0..1..1
..0..0..0..0..0....0..0..0..0..1....0..0..0..1..0....0..0..0..1..1
..0..0..0..0..0....0..0..0..0..1....1..0..1..0..1....0..0..1..1..1
..0..0..0..1..1....1..0..0..0..1....0..1..0..1..1....0..0..1..1..1
..0..0..0..1..1....0..1..1..1..1....1..0..1..1..1....0..0..1..1..1
..0..0..1..1..1....0..1..1..1..1....0..1..1..1..1....0..0..1..1..1
..0..1..1..1..1....0..1..1..1..1....1..1..1..1..1....1..1..1..1..1

R. H. Hardin, Table of n, a(n) for n = 1..210

Empirical: a(n) = 6*a(n-1) -8*a(n-2) -19*a(n-3) +61*a(n-4) -32*a(n-5) -70*a(n-6) +104*a(n-7) -30*a(n-8) -30*a(n-9) +24*a(n-10) -5*a(n-11) for n>15

A250736 Number of (7+1)X(n+1) 0..1 arrays with nondecreasing x(i,j)+x(i,j-1) in the i direction and nondecreasing min(x(i,j),x(i-1,j)) in the j direction.

Original entry on oeis.org

275, 513, 1418, 3807, 9728, 23941, 57397, 135645, 317769, 741367, 1725118, 4010707, 9318138, 21648961, 50290988, 116846565, 271483896, 630867956, 1466032586, 3407186212, 7918751613, 18405536442, 42780485640, 99440346555, 231144060876

Offset: 1

R. H. Hardin, Nov 27 2014

nonn

Row 7 of A250729

			Some solutions for n=4
..0..0..0..0..0....0..0..0..0..0....0..0..0..0..1....0..0..0..0..0
..0..0..0..0..1....0..0..0..0..1....0..0..0..0..1....0..0..0..0..1
..0..0..0..0..1....0..0..0..0..1....0..0..0..1..1....0..0..0..0..1
..0..0..0..0..1....0..0..0..0..1....0..0..0..1..1....0..0..1..1..1
..0..0..0..0..1....0..0..0..0..1....0..1..1..1..1....0..0..1..1..1
..0..0..0..0..1....1..0..1..0..1....0..1..1..1..1....0..0..1..1..1
..1..0..0..0..1....0..1..0..1..1....1..1..1..1..1....0..1..1..1..1
..0..1..0..1..0....1..0..1..1..1....1..1..1..1..1....0..1..1..1..1

R. H. Hardin, Table of n, a(n) for n = 1..210

Empirical: a(n) = 7*a(n-1) -13*a(n-2) -18*a(n-3) +95*a(n-4) -89*a(n-5) -102*a(n-6) +264*a(n-7) -143*a(n-8) -94*a(n-9) +150*a(n-10) -60*a(n-11) -a(n-12) +6*a(n-13) -a(n-14) for n>19

cp's OEIS Frontend

A250733 Number of (4+1) X (n+1) 0..1 arrays with nondecreasing x(i,j)+x(i,j-1) in the i direction and nondecreasing min(x(i,j),x(i-1,j)) in the j direction.

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A250734 Number of (5+1) X (n+1) 0..1 arrays with nondecreasing x(i,j)+x(i,j-1) in the i direction and nondecreasing min(x(i,j),x(i-1,j)) in the j direction.

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A250735 Number of (6+1)X(n+1) 0..1 arrays with nondecreasing x(i,j)+x(i,j-1) in the i direction and nondecreasing min(x(i,j),x(i-1,j)) in the j direction.

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A250736 Number of (7+1)X(n+1) 0..1 arrays with nondecreasing x(i,j)+x(i,j-1) in the i direction and nondecreasing min(x(i,j),x(i-1,j)) in the j direction.

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