A203865 Number of (n+1) X 4 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.

10077, 210190, 2935262, 31521422, 269967062, 1959924899, 12355307346, 69538725100, 355086812343, 1670161159444, 7313802432208, 30100371968112, 117281027993050, 435371655084564, 1547853430649401, 5294106139481541

Offset

1,1

Comments

Column 3 of A203870.

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

Empirical: a(n) = 25*a(n-1) -259*a(n-2) +1294*a(n-3) -1618*a(n-4) -16376*a(n-5) +87676*a(n-6) -75730*a(n-7) -751425*a(n-8) +2565849*a(n-9) +812320*a(n-10) -20996639*a(n-11) +31130911*a(n-12) +80257744*a(n-13) -291173817*a(n-14) -26997717*a(n-15) +1411991143*a(n-16) -1477836644*a(n-17) -4165787546*a(n-18) +9618742270*a(n-19) +5824224632*a(n-20) -36360744996*a(n-21) +11205716945*a(n-22) +95571201239*a(n-23) -97288836653*a(n-24) -176356361340*a(n-25) +340751653292*a(n-26) +192687651290*a(n-27) -824451215886*a(n-28) +52212432780*a(n-29) +1519977116954*a(n-30) -812112069792*a(n-31) -2182967672024*a(n-32) +2218508974558*a(n-33) +2379774678699*a(n-34) -4070714014283*a(n-35) -1717934481745*a(n-36) +5796666696208*a(n-37) +161140694113*a(n-38) -6705442004697*a(n-39) +1836071025274*a(n-40) +6398346741415*a(n-41) -3538563182028*a(n-42) -5023727430649*a(n-43) +4355719731045*a(n-44) +3168660914610*a(n-45) -4156028978280*a(n-46) -1488318186992*a(n-47) +3253968125215*a(n-48) +370641922357*a(n-49) -2139168648003*a(n-50) +152414762000*a(n-51) +1191920072246*a(n-52) -271439976460*a(n-53) -563863862941*a(n-54) +211007519029*a(n-55) +225491052379*a(n-56) -118861043802*a(n-57) -75357095588*a(n-58) +53367304132*a(n-59) +20561888968*a(n-60) -19721397416*a(n-61) -4357039714*a(n-62) +6066905068*a(n-63) +621528919*a(n-64) -1555994597*a(n-65) -18621388*a(n-66) +331052047*a(n-67) -19859515*a(n-68) -57810360*a(n-69) +6876783*a(n-70) +8146031*a(n-71) -1371703*a(n-72) -902794*a(n-73) +190116*a(n-74) +75674*a(n-75) -18702*a(n-76) -4502*a(n-77) +1257*a(n-78) +169*a(n-79) -52*a(n-80) -3*a(n-81) +a(n-82) for n>89.

Example

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

Crossrefs

Cf. A203870.

Sequence in context: A252200 A234773 A348698 * A145836 A190293 A179729

Adjacent sequences: A203862 A203863 A203864 * A203866 A203867 A203868

Keyword

nonn

Author

R. H. Hardin, Jan 07 2012

Status

approved