OFFSET
1,1
COMMENTS
Table starts
....9...16....25....36....49....64....81...100...121...144...169....196....225
...19...34....53....76...103...134...169...208...251...298...349....404....463
...39...70...109...156...211...274...345...424...511...606...709....820....939
...79..142...221...316...427...554...697...856..1031..1222..1429...1652...1891
..159..286...445...636...859..1114..1401..1720..2071..2454..2869...3316...3795
..319..574...893..1276..1723..2234..2809..3448..4151..4918..5749...6644...7603
..639.1150..1789..2556..3451..4474..5625..6904..8311..9846.11509..13300..15219
.1279.2302..3581..5116..6907..8954.11257.13816.16631.19702.23029..26612..30451
.2559.4606..7165.10236.13819.17914.22521.27640.33271.39414.46069..53236..60915
.5119.9214.14333.20476.27643.35834.45049.55288.66551.78838.92149.106484.121843
LINKS
R. H. Hardin, Table of n, a(n) for n = 1..880
FORMULA
Empirical: T(n,k) = 2^(n-1)*k^2 + (5*2^(n-1)-1)*k + 2^(n+1)
Empirical for column k:
k=1: a(n) = 3*a(n-1) -2*a(n-2); also a(n) = 2^(n-1) +(5*2^(n-1) -1) +2^(n+1)
k=2: a(n) = 3*a(n-1) -2*a(n-2); also a(n) = 2^(n-1)*4 +(5*2^(n-1) -1)*2 +2^(n+1)
k=3: a(n) = 3*a(n-1) -2*a(n-2); also a(n) = 2^(n-1)*9 +(5*2^(n-1) -1)*3 +2^(n+1)
k=4: a(n) = 3*a(n-1) -2*a(n-2); also a(n) = 2^(n-1)*16 +(5*2^(n-1) -1)*4 +2^(n+1)
k=5: a(n) = 3*a(n-1) -2*a(n-2); also a(n) = 2^(n-1)*25 +(5*2^(n-1) -1)*5 +2^(n+1)
k=6: a(n) = 3*a(n-1) -2*a(n-2); also a(n) = 2^(n-1)*36 +(5*2^(n-1) -1)*6 +2^(n+1)
k=7: a(n) = 3*a(n-1) -2*a(n-2); also a(n) = 2^(n-1)*49 +(5*2^(n-1) -1)*7 +2^(n+1)
Empirical for row n:
n=1: a(n) = 1*n^2 + 4*n + 4
n=2: a(n) = 2*n^2 + 9*n + 8
n=3: a(n) = 4*n^2 + 19*n + 16
n=4: a(n) = 8*n^2 + 39*n + 32
n=5: a(n) = 16*n^2 + 79*n + 64
n=6: a(n) = 32*n^2 + 159*n + 128
n=7: a(n) = 64*n^2 + 319*n + 256
EXAMPLE
Some solutions for n=4 k=4
..1..1..0..1..1....0..0..0..0..0....0..0..0..0..0....1..1..1..0..0
..0..0..0..1..1....1..1..1..1..1....1..1..1..1..1....0..0..0..0..0
..0..0..0..1..1....1..1..1..1..1....0..0..0..0..0....0..0..0..0..0
..0..0..0..1..1....0..0..0..0..0....1..1..1..1..1....1..1..1..1..1
..0..0..0..1..1....0..1..1..1..1....1..1..1..1..1....0..0..0..1..1
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Nov 26 2014
STATUS
approved