A251028 T(n,k)=Number of (n+1)X(k+1) 0..3 arrays with no 2X2 subblock having the sum of its diagonal elements greater than the maximum of its antidiagonal elements

110, 526, 526, 1966, 2546, 1966, 6321, 8207, 8207, 6321, 18330, 23404, 20608, 23404, 18330, 49481, 60044, 51347, 51347, 60044, 49481, 126955, 144737, 118871, 119632, 118871, 144737, 126955, 314337, 334167, 272547, 257578, 257578, 272547, 334167

Offset

1,1

Comments

Table starts

.....110.....526....1966.....6321....18330....49481...126955....314337

.....526....2546....8207....23404....60044...144737...334167....755336

....1966....8207...20608....51347...118871...272547...608267...1356939

....6321...23404...51347...119632...257578...563271..1199576...2590598

...18330...60044..118871...257578...516684..1078862..2203974...4638560

...49481..144737..272547...563271..1078862..2160510..4230166...8587303

..126955..334167..608267..1199576..2203974..4230166..7948184..15543033

..314337..755336.1356939..2590598..4638560..8587303.15543033..29146692

..759223.1690491.3017800..5601754..9823382.17595371.30783775..55366008

.1803024.3781186.6755296.12305560.21323795.37245814.63428115.109773400

Links

R. H. Hardin, Table of n, a(n) for n = 1..391

Formula

Empirical for column k:

k=1: a(n) = 7*a(n-1) -18*a(n-2) +17*a(n-3) +10*a(n-4) -39*a(n-5) +38*a(n-6) -17*a(n-7) +3*a(n-8)

k=2: a(n) = 8*a(n-1) -25*a(n-2) +35*a(n-3) -7*a(n-4) -49*a(n-5) +77*a(n-6) -55*a(n-7) +20*a(n-8) -3*a(n-9) for n>13

k=3: a(n) = 8*a(n-1) -25*a(n-2) +35*a(n-3) -7*a(n-4) -49*a(n-5) +77*a(n-6) -55*a(n-7) +20*a(n-8) -3*a(n-9) for n>14

k=4: a(n) = 8*a(n-1) -25*a(n-2) +35*a(n-3) -7*a(n-4) -49*a(n-5) +77*a(n-6) -55*a(n-7) +20*a(n-8) -3*a(n-9) for n>14

k=5: a(n) = 8*a(n-1) -25*a(n-2) +35*a(n-3) -7*a(n-4) -49*a(n-5) +77*a(n-6) -55*a(n-7) +20*a(n-8) -3*a(n-9) for n>14

k=6: a(n) = 8*a(n-1) -25*a(n-2) +35*a(n-3) -7*a(n-4) -49*a(n-5) +77*a(n-6) -55*a(n-7) +20*a(n-8) -3*a(n-9) for n>14

k=7: a(n) = 8*a(n-1) -25*a(n-2) +35*a(n-3) -7*a(n-4) -49*a(n-5) +77*a(n-6) -55*a(n-7) +20*a(n-8) -3*a(n-9) for n>14

Example

Some solutions for n=4 k=4
..0..0..0..0..2....0..3..3..3..3....0..0..0..0..3....0..0..2..2..3
..0..0..0..0..2....0..0..0..0..0....0..0..0..0..3....0..0..1..0..1
..2..2..2..2..2....2..2..2..2..2....0..0..0..0..2....0..0..1..0..1
..1..0..0..0..0....0..0..0..0..0....1..0..0..0..2....1..0..1..0..1
..3..2..1..1..0....3..3..3..1..0....3..0..0..0..2....2..0..1..0..0

Crossrefs

Sequence in context: A209372 A285984 A158539 * A251021 A251030 A156852

Adjacent sequences: A251025 A251026 A251027 * A251029 A251030 A251031

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 29 2014

Status

approved