A268886 T(n,k)=Number of nXk binary arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling two exactly once.

0, 1, 0, 2, 5, 0, 5, 14, 20, 0, 10, 54, 84, 71, 0, 20, 158, 501, 462, 235, 0, 38, 475, 2190, 4133, 2418, 744, 0, 71, 1340, 9996, 27130, 31956, 12252, 2285, 0, 130, 3740, 42362, 186732, 317966, 236960, 60666, 6865, 0, 235, 10204, 178400, 1187838, 3283890

Offset: 1

Author

R. H. Hardin, Feb 15 2016

Keywords

• nonn
• tabl

Comments

Table starts

.0.....1.......2.........5..........10............20..............38

.0.....5......14........54.........158...........475............1340

.0....20......84.......501........2190..........9996...........42362

.0....71.....462......4133.......27130........186732.........1187838

.0...235....2418.....31956......317966.......3283890........31427480

.0...744...12252....236960.....3596174......55491832.......800733668

.0..2285...60666...1706732....39670270.....911930096.....19876401224

.0..6865..295230..12034000...429588382...14681855846....483987898760

.0.20284.1417452..83485488..4585939726..232688402028..11611969197776

.0.59155.6732102.571836176.48401059362.3642322709900.275345016177616

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..799

Crossrefs

Column 2 is A054444(n-1).

Row 1 is A001629.

Formula

Empirical for column k:

k=1: a(n) = a(n-1)

k=2: a(n) = 6*a(n-1) -11*a(n-2) +6*a(n-3) -a(n-4)

k=3: a(n) = 10*a(n-1) -31*a(n-2) +30*a(n-3) -9*a(n-4)

k=4: a(n) = 16*a(n-1) -88*a(n-2) +200*a(n-3) -208*a(n-4) +96*a(n-5) -16*a(n-6) for n>7

k=5: [order 8] for n>9

k=6: [order 10] for n>12

k=7: [order 14] for n>16

Empirical for row n:

n=1: a(n) = 2*a(n-1) +a(n-2) -2*a(n-3) -a(n-4)

n=2: a(n) = 2*a(n-1) +5*a(n-2) -4*a(n-3) -11*a(n-4) -6*a(n-5) -a(n-6)

n=3: [order 9]

n=4: [order 16]

n=5: [order 26]

n=6: [order 42]

n=7: [order 68]