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

1,4

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

Links

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

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]

Example

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

Crossrefs

Column 2 is A054444(n-1).

Row 1 is A001629.

Sequence in context: A196816 A058204 A242969 * A090625 A021403 A299623

Adjacent sequences: A268883 A268884 A268885 * A268887 A268888 A268889

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 15 2016

Status

approved