A224568 T(n,k)=Number of (n+3)X(k+3) 0..1 matrices with each 4X4 subblock idempotent

452, 370, 370, 512, 340, 512, 739, 428, 428, 739, 990, 517, 514, 517, 990, 1345, 611, 629, 629, 611, 1345, 1852, 775, 728, 752, 728, 775, 1852, 2659, 1044, 929, 861, 861, 929, 1044, 2659, 3846, 1383, 1232, 1091, 974, 1091, 1232, 1383, 3846, 5589, 1808

Offset

1,1

Comments

Table starts

..452..370..512..739..990.1345.1852.2659.3846.5589..8064.11675.16954.24757

..370..340..428..517..611..775.1044.1383.1808.2373..3190..4323..5868..7946

..512..428..514..629..728..929.1232.1627.2095.2739..3658..4945..6670..9010

..739..517..629..752..861.1091.1433.1871.2390.3108..4136..5571..7493.10098

..990..611..728..861..974.1233.1614.2099.2665.3459..4600..6193..8316.11198

.1345..775..929.1091.1233.1550.1997.2558.3206.4115..5408..7202..9577.12793

.1852.1044.1232.1433.1614.1997.2526.3175.3917.4951..6416..8429.11076.14646

.2659.1383.1627.1871.2099.2558.3175.3918.4764.5935..7582..9826.12763.16709

.3846.1808.2095.2390.2665.3206.3917.4764.5716.7032..8871.11362.14599.18939

.5589.2373.2739.3108.3459.4115.4951.5935.7032.8536.10610.13395.16987.21782

Links

R. H. Hardin, Table of n, a(n) for n = 1..1798

Formula

Empirical for column k:

k=1: a(n) = 3*a(n-1) -3*a(n-2) +a(n-3) +a(n-4) -2*a(n-5) +2*a(n-6) -2*a(n-7) +a(n-8) for n>10

k=2: a(n) = 2*a(n-1) -a(n-2) +a(n-3) -2*a(n-5) +a(n-6) -2*a(n-7) +2*a(n-8) +a(n-11) -a(n-12) for n>15

k=3: a(n) = 3*a(n-1) -2*a(n-2) -2*a(n-3) +4*a(n-4) -3*a(n-5) +2*a(n-7) -a(n-8) for n>10

k=4: a(n) = 4*a(n-1) -7*a(n-2) +8*a(n-3) -6*a(n-4) +a(n-5) +3*a(n-6) -4*a(n-7) +3*a(n-8) -a(n-9) for n>11

k=5: a(n) = 3*a(n-1) -2*a(n-2) -2*a(n-3) +4*a(n-4) -3*a(n-5) +2*a(n-7) -a(n-8) for n>10

k=6: a(n) = 3*a(n-1) -3*a(n-2) +a(n-3) +2*a(n-4) -5*a(n-5) +4*a(n-6) -a(n-7) -a(n-8) +2*a(n-9) -a(n-10) for n>12

k=7: a(n) = 3*a(n-1) -2*a(n-2) -2*a(n-3) +4*a(n-4) -3*a(n-5) +2*a(n-7) -a(n-8) for n>10

k=8: a(n) = 4*a(n-1) -7*a(n-2) +8*a(n-3) -6*a(n-4) +a(n-5) +3*a(n-6) -4*a(n-7) +3*a(n-8) -a(n-9) for n>11

k=9: a(n) = 3*a(n-1) -2*a(n-2) -2*a(n-3) +4*a(n-4) -3*a(n-5) +2*a(n-7) -a(n-8) for n>10

k=10: a(n) = 3*a(n-1) -3*a(n-2) +a(n-3) +2*a(n-4) -5*a(n-5) +4*a(n-6) -a(n-7) -a(n-8) +2*a(n-9) -a(n-10) for n>12

k=11: a(n) = 3*a(n-1) -2*a(n-2) -2*a(n-3) +4*a(n-4) -3*a(n-5) +2*a(n-7) -a(n-8) for n>10

k=12: a(n) = 4*a(n-1) -7*a(n-2) +8*a(n-3) -6*a(n-4) +a(n-5) +3*a(n-6) -4*a(n-7) +3*a(n-8) -a(n-9) for n>11

Example

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

Crossrefs

Sequence in context: A066322 A128922 A224560 * A224561 A116308 A183636

Adjacent sequences: A224565 A224566 A224567 * A224569 A224570 A224571

Keyword

nonn,tabl

Author

R. H. Hardin Apr 10 2013

Status

approved