A157727 -id:A157727 - cp's OEIS frontend

A258316 T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with each 2X2 subblock having clockwise pattern 0000 or 0011.

5, 7, 7, 10, 9, 10, 15, 12, 12, 15, 23, 17, 15, 17, 23, 36, 25, 20, 20, 25, 36, 57, 38, 28, 25, 28, 38, 57, 91, 59, 41, 33, 33, 41, 59, 91, 146, 93, 62, 46, 41, 46, 62, 93, 146, 235, 148, 96, 67, 54, 54, 67, 96, 148, 235, 379, 237, 151, 101, 75, 67, 75, 101, 151, 237, 379, 612

Offset: 1

R. H. Hardin, Jun 29 2015

Table starts
...5...7..10..15..23..36..57..91.146.235.379.612..989.1599.2586.4183.6767.10948
...7...9..12..17..25..38..59..93.148.237.381.614..991.1601.2588.4185.6769.10950
..10..12..15..20..28..41..62..96.151.240.384.617..994.1604.2591.4188.6772.10953
..15..17..20..25..33..46..67.101.156.245.389.622..999.1609.2596.4193.6777.10958
..23..25..28..33..41..54..75.109.164.253.397.630.1007.1617.2604.4201.6785.10966
..36..38..41..46..54..67..88.122.177.266.410.643.1020.1630.2617.4214.6798.10979
..57..59..62..67..75..88.109.143.198.287.431.664.1041.1651.2638.4235.6819.11000
..91..93..96.101.109.122.143.177.232.321.465.698.1075.1685.2672.4269.6853.11034
.146.148.151.156.164.177.198.232.287.376.520.753.1130.1740.2727.4324.6908.11089
.235.237.240.245.253.266.287.321.376.465.609.842.1219.1829.2816.4413.6997.11178
Apparently: put 1s in some number of nonadjacent columns or put 1s in some number of nonadjacent rows

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

R. H. Hardin, Table of n, a(n) for n = 1..1104

Column 1 is A018910
Column 2 is A157727(n+3)
Column 3 is A187107(n+3)
Diagonal is A001595(n+2)
Superdiagonal 1 is A000071(n+5)
Superdiagonal 2 is A001610(n+3)
Superdiagonal 3 is A001595(n+4)
Superdiagonal 5 is A022308(n+5)
Superdiagonal 6 is A022319(n+5)
Superdiagonal 7 is A022407(n+5)
Superdiagonal 9 is A022323(n+7)

Empirical: T(n,k) = Fibonacci(n+3) +Fibonacci(k+3) -1

Empirical for rows, columns and nw-se diagonals: a(n) = 2*a(n-1) -a(n-3)

A217762 Square array T, read by antidiagonals: T(n,k) = F(n) + 2*F(k) where F(n) is the n-th Fibonacci number.

Original entry on oeis.org

0, 2, 1, 2, 3, 1, 4, 3, 3, 2, 6, 5, 3, 4, 3, 10, 7, 5, 4, 5, 5, 16, 11, 7, 6, 5, 7, 8, 26, 17, 11, 8, 7, 7, 10, 13, 42, 27, 17, 12, 9, 9, 10, 15, 21, 68, 43, 27, 18, 13, 11, 12, 15, 23, 34, 110, 69, 43, 28, 19, 15, 14, 17, 23, 36, 55, 178, 111, 69, 44, 29, 21

Offset: 0

Philippe Deléham, Apr 07 2013

			Square array begins:
...0....2....2....4....6...10...16...26...42...
...1....3....3....5....7...11...17...27...43...
...1....3....3....5....7...11...17...27...43...
...2....4....4....6....8...12...18...28...44...
...3....5....5....7....9...13...19...29...45...
...5....7....7....9...11...15...21...31...47...
...8...10...10...12...14...18...24...34...50...
..13...15...15...17...19...23...29...39...55...
..21...23...23...25...27...31...37...47...63...
..34...36...36...38...40...44...50...60...76...
..55...57...57...59...61...65...71...81...97...
..89...91...91...93...95...99..105..115..131...
.144..146..146..148..150..154..160..170..186...
...

Cf. A000045

T(n,0) = A000045(n).
T(1,k) = A001588(k).
T(n,1) = T(n,2) = A157725(n).
T(n,3) = A157727(n).
T(n,n)= A022086(n) = 3*A000045(n).
T(n+1,n) = A000032(n+1) = A000204(n+1).
T(n+2,n) = A000285(n).
T(n+3,n) = A013655(n+1) = A001060(n+1).
T(n+4,n) = A021120(n).
T(n+5,n) = A022088(n+2) = 5*A000045(n+2).
T(n+6,n) = A022097(n+2).
T(n+7,n) = A022122(n+2).
T(n+8,n) = 3*A013655(n+2).
T(n+9,n) = A097657(n+2).
T(n+10,n) = A022118(n+4).
T(n,n+1) = A000045(n+3).
T(n,n+2) = A013655(n+1) = A001060(n+1).
T(n,n+3) = A000032(n+3).
T(n,n+4) = A022095(n+2).
T(n,n+5) = A022120(n+2).
T(n,n+6) = A022136(n+2).
T(n,n+7) = A022098(n+4).
T(n,n+8) = A022380(n+4).
T(n,n+9) = A206419(n+6).
Sum(T(n-k,k), 0<=k<=n) = 3*A000071(n+2).

cp's OEIS Frontend

A258316 T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with each 2X2 subblock having clockwise pattern 0000 or 0011.

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