A224606 T(n,k)=Number of (n+2)X(k+2) 0..2 matrices with each 3X3 subblock idempotent

122, 178, 178, 297, 272, 297, 416, 371, 371, 416, 628, 449, 482, 449, 628, 1045, 630, 571, 571, 630, 1045, 1694, 894, 782, 666, 782, 894, 1694, 2668, 1221, 1086, 906, 906, 1086, 1221, 2668, 4265, 1707, 1455, 1247, 1202, 1247, 1455, 1707, 4265, 6922, 2440

Offset

1,1

Comments

Table starts

..122..178..297..416..628.1045.1694.2668..4265..6922.11196.18035.29122.47134

..178..272..371..449..630..894.1221.1707..2440..3476..4979..7189.10414.15114

..297..371..482..571..782.1086.1455.2010..2843..4018..5720..8226.11877.17199

..416..449..571..666..906.1247.1657.2280..3216..4533..6443..9258.13358.19335

..628..630..782..906.1202.1609.2091.2817..3895..5397..7564.10745.15361.22074

.1045..894.1086.1247.1609.2092.2656.3497..4731..6434..8878.12451.17617.25112

.1694.1221.1455.1657.2091.2656.3308.4272..5672..7588.10325.14312.20058.28377

.2668.1707.2010.2280.2817.3497.4272.5398..7007..9183.12266.16728.23125.32353

.4265.2440.2843.3216.3895.4731.5672.7007..8876.11367.14857.19863.26990.37220

.6922.3476.4018.4533.5397.6434.7588.9183.11367.14232.18194.23817.31757.43086

Links

R. H. Hardin, Table of n, a(n) for n = 1..1403

Formula

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..7+: 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..1..0..0..0..0....1..0..0..0..0..0....0..1..0..0..0..1....1..0..0..0..0..0
..0..0..0..0..0..0....0..0..0..0..0..0....0..1..0..0..0..1....1..0..0..0..0..0
..0..0..0..0..0..0....0..0..0..0..0..0....0..1..0..0..0..1....1..0..0..0..0..0
..0..0..0..0..0..0....0..0..0..0..0..0....0..1..0..0..0..1....0..0..0..0..0..0
..1..2..1..1..1..1....0..0..0..0..0..0....0..0..0..0..0..1....0..0..0..0..1..1

Crossrefs

Sequence in context: A077030 A280733 A309760 * A224599 A207147 A222578

Adjacent sequences: A224603 A224604 A224605 * A224607 A224608 A224609

Keyword

nonn,tabl

Author

R. H. Hardin Apr 11 2013

Status

approved