A224559 T(n,k)=Number of (n+2)X(k+2) 0..1 matrices with each 3X3 subblock idempotent

50, 70, 70, 113, 94, 113, 172, 133, 133, 172, 263, 174, 180, 174, 263, 418, 246, 230, 230, 246, 418, 669, 351, 320, 286, 320, 351, 669, 1064, 492, 451, 395, 395, 451, 492, 1064, 1699, 693, 620, 551, 540, 551, 620, 693, 1699, 2734, 992, 866, 749, 740, 740, 749, 866

Offset

1,1

Comments

Table starts

...50...70..113..172..263..418..669.1064.1699.2734..4409..7108.11471.18538

...70...94..133..174..246..351..492..693..992.1418..2036..2937..4253..6169

..113..133..180..230..320..451..620..866.1229.1746..2493..3586..5178..7498

..172..174..230..286..395..551..749.1041.1473.2086..2973..4273..6166..8925

..263..246..320..395..540..740..988.1351.1881.2623..3689..5243..7494.10763

..418..351..451..551..740..992.1298.1742.2382.3267..4530..6362..9003.12826

..669..492..620..749..988.1298.1668.2201.2961.4001..5477..7609.10670.15089

.1064..693..866.1041.1351.1742.2201.2852.3765.4997..6729..9212.12754.17844

.1699..992.1229.1473.1881.2382.2961.3765.4870.6337..8374.11265.15355.21197

.2734.1418.1746.2086.2623.3267.4001.4997.6337.8086.10481.13841.18550.25229

Links

R. H. Hardin, Table of n, a(n) for n = 1..1566

Formula

Empirical for diagonal:

k=0: a(n) = 6*a(n-1) -15*a(n-2) +23*a(n-3) -30*a(n-4) +36*a(n-5) -34*a(n-6) +27*a(n-7) -21*a(n-8) +13*a(n-9) -6*a(n-10) +3*a(n-11) -a(n-12) for n>14

Empirical for column k:

k=1: a(n) = 3*a(n-1) -3*a(n-2) +2*a(n-3) -a(n-4) -a(n-5) +a(n-6) for n>7

k=2: a(n) = 3*a(n-1) -2*a(n-2) -a(n-3) +a(n-4) -a(n-5) +2*a(n-6) -a(n-7) for n>9

k=3..12+: a(n) = 4*a(n-1) -6*a(n-2) +5*a(n-3) -4*a(n-4) +3*a(n-5) -a(n-6) for n>8

Example

Some solutions for n=3 k=4
..1..0..0..0..0..0....1..1..1..1..1..1....1..1..1..1..1..0....1..0..0..0..0..1
..1..0..0..0..0..0....0..0..0..0..0..0....0..0..0..0..0..0....1..0..0..0..0..0
..1..0..0..0..0..0....0..0..0..0..0..0....0..0..0..0..0..0....1..0..0..0..0..1
..1..0..0..0..0..0....0..1..1..1..1..1....0..0..0..0..0..0....0..0..0..0..0..1
..1..0..0..0..0..1....0..0..0..0..0..0....0..0..1..1..1..1....0..0..0..0..0..1

Crossrefs

Sequence in context: A335233 A180103 A102803 * A272607 A224552 A039473

Adjacent sequences: A224556 A224557 A224558 * A224560 A224561 A224562

Keyword

nonn,tabl

Author

R. H. Hardin Apr 10 2013

Status

approved