A203864 - OEIS

%I #7 Mar 07 2022 14:21:48

%S 1648,21635,210190,1605552,10500903,59962757,309154358,1459797487,

%T 6416948063,26519347624,104007127796,389733297547,1403705680053,

%U 4882521376349,16468445276261,54047747618910,173099841345451

%N Number of (n+1) X 3 0..4 arrays with column and row pair sums b(i,j) = a(i,j)+a(i,j-1) and c(i,j) = a(i,j)+a(i-1,j) nondecreasing in column and row directions, respectively.

%C Column 2 of A203870.

%H R. H. Hardin, <a href="/A203864/b203864.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 24*a(n-1) -245*a(n-2) +1304*a(n-3) -3072*a(n-4) -4062*a(n-5) +47872*a(n-6) -106234*a(n-7) -95560*a(n-8) +910050*a(n-9) -1212323*a(n-10) -2512006*a(n-11) +9247443*a(n-12) -2655670*a(n-13) -29744182*a(n-14) +41816738*a(n-15) +43950572*a(n-16) -151060270*a(n-17) +22766647*a(n-18) +312572526*a(n-19) -268708090*a(n-20) -394548406*a(n-21) +688387549*a(n-22) +221758570*a(n-23) -1083905449*a(n-24) +227614160*a(n-25) +1188977774*a(n-26) -729855744*a(n-27) -921456902*a(n-28) +991229158*a(n-29) +466040322*a(n-30) -908030702*a(n-31) -87892667*a(n-32) +616001236*a(n-33) -87488176*a(n-34) -319063060*a(n-35) +104460481*a(n-36) +127050816*a(n-37) -63202323*a(n-38) -38574760*a(n-39) +26334347*a(n-40) +8712758*a(n-41) -8075877*a(n-42) -1388146*a(n-43) +1850933*a(n-44) +136584*a(n-45) -314594*a(n-46) -4188*a(n-47) +38598*a(n-48) -774*a(n-49) -3240*a(n-50) +102*a(n-51) +167*a(n-52) -4*a(n-53) -4*a(n-54) for n>57.

%e Some solutions for n=4

%e ..1..2..2....4..0..3....2..4..4....2..4..2....4..4..4....3..1..0....4..3..3

%e ..4..3..4....0..4..4....4..4..4....4..2..4....4..4..4....1..3..4....3..4..4

%e ..3..4..3....0..4..4....4..4..4....2..4..2....4..4..4....0..4..3....3..4..4

%e ..4..3..4....4..4..4....4..4..4....4..2..4....4..4..4....1..3..4....3..4..4

%e ..3..4..3....4..4..4....4..4..4....2..4..2....4..4..4....1..3..4....4..4..4

%Y Cf. A203870.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 07 2012