A250656 - OEIS

%I #4 Nov 26 2014 12:54:43

%S 9,16,19,25,34,39,36,53,70,79,49,76,109,142,159,64,103,156,221,286,

%T 319,81,134,211,316,445,574,639,100,169,274,427,636,893,1150,1279,121,

%U 208,345,554,859,1276,1789,2302,2559,144,251,424,697,1114,1723,2556,3581

%N T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing min(x(i,j),x(i-1,j)) in the j direction

%C Table starts

%C ....9...16....25....36....49....64....81...100...121...144...169....196....225

%C ...19...34....53....76...103...134...169...208...251...298...349....404....463

%C ...39...70...109...156...211...274...345...424...511...606...709....820....939

%C ...79..142...221...316...427...554...697...856..1031..1222..1429...1652...1891

%C ..159..286...445...636...859..1114..1401..1720..2071..2454..2869...3316...3795

%C ..319..574...893..1276..1723..2234..2809..3448..4151..4918..5749...6644...7603

%C ..639.1150..1789..2556..3451..4474..5625..6904..8311..9846.11509..13300..15219

%C .1279.2302..3581..5116..6907..8954.11257.13816.16631.19702.23029..26612..30451

%C .2559.4606..7165.10236.13819.17914.22521.27640.33271.39414.46069..53236..60915

%C .5119.9214.14333.20476.27643.35834.45049.55288.66551.78838.92149.106484.121843

%H R. H. Hardin, <a href="/A250656/b250656.txt">Table of n, a(n) for n = 1..880</a>

%F Empirical: T(n,k) = 2^(n-1)*k^2 + (5*2^(n-1)-1)*k + 2^(n+1)

%F Empirical for column k:

%F 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)

%F 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)

%F 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)

%F 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)

%F 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)

%F 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)

%F 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)

%F Empirical for row n:

%F n=1: a(n) = 1*n^2 + 4*n + 4

%F n=2: a(n) = 2*n^2 + 9*n + 8

%F n=3: a(n) = 4*n^2 + 19*n + 16

%F n=4: a(n) = 8*n^2 + 39*n + 32

%F n=5: a(n) = 16*n^2 + 79*n + 64

%F n=6: a(n) = 32*n^2 + 159*n + 128

%F n=7: a(n) = 64*n^2 + 319*n + 256

%e Some solutions for n=4 k=4

%e ..1..1..0..1..1....0..0..0..0..0....0..0..0..0..0....1..1..1..0..0

%e ..0..0..0..1..1....1..1..1..1..1....1..1..1..1..1....0..0..0..0..0

%e ..0..0..0..1..1....1..1..1..1..1....0..0..0..0..0....0..0..0..0..0

%e ..0..0..0..1..1....0..0..0..0..0....1..1..1..1..1....1..1..1..1..1

%e ..0..0..0..1..1....0..1..1..1..1....1..1..1..1..1....0..0..0..1..1

%Y Column 1 is A052549(n+1)

%Y Column 2 is A176449

%Y Column 3 is A156127(n+1)

%Y Column 4 is A048487(n+2)

%Y Row 1 is A000290(n+2)

%Y Row 2 is A168244(n+3)

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Nov 26 2014