A250430 Number of (n+1)X(6+1) 0..1 arrays with nondecreasing sum of every two consecutive values in every row and column

400, 3000, 22500, 105000, 490000, 1715000, 6002500, 17287200, 49787136, 124467840, 311169600, 698544000, 1568160000, 3234330000, 6670805625, 12847477500, 24743290000, 45032787800, 81959673796, 142244061960

Offset

1,1

Comments

Column 6 of A250432.

Links

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

Formula

Empirical: a(n) = 2*a(n-1) +12*a(n-2) -26*a(n-3) -65*a(n-4) +156*a(n-5) +208*a(n-6) -572*a(n-7) -429*a(n-8) +1430*a(n-9) +572*a(n-10) -2574*a(n-11) -429*a(n-12) +3432*a(n-13) -3432*a(n-15) +429*a(n-16) +2574*a(n-17) -572*a(n-18) -1430*a(n-19) +429*a(n-20) +572*a(n-21) -208*a(n-22) -156*a(n-23) +65*a(n-24) +26*a(n-25) -12*a(n-26) -2*a(n-27) +a(n-28)

Empirical for n mod 2 = 0: a(n) = (1/339738624)*n^14 + (13/56623104)*n^13 + (697/84934656)*n^12 + (2521/14155776)*n^11 + (55639/21233664)*n^10 + (97807/3538944)*n^9 + (1143251/5308416)*n^8 + (1113683/884736)*n^7 + (1838411/331776)*n^6 + (505009/27648)*n^5 + (919427/20736)*n^4 + (265331/3456)*n^3 + (4297/48)*n^2 + (377/6)*n + 20

Empirical for n mod 2 = 1: a(n) = (1/339738624)*n^14 + (13/56623104)*n^13 + (2795/339738624)*n^12 + (5081/28311552)*n^11 + (301475/113246208)*n^10 + (178667/6291456)*n^9 + (76312715/339738624)*n^8 + (18940223/14155776)*n^7 + (2048631355/339738624)*n^6 + (1158380483/56623104)*n^5 + (647048923/12582912)*n^4 + (292086865/3145728)*n^3 + (477479275/4194304)*n^2 + (177888375/2097152)*n + (121550625/4194304).

a(n+1) = A202097(n). - R. J. Mathar, Dec 02 2014

Example

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

Crossrefs

Sequence in context: A250847 A043400 A038483 * A281808 A192076 A006764

Adjacent sequences: A250427 A250428 A250429 * A250431 A250432 A250433

Keyword

nonn

Author

R. H. Hardin, Nov 22 2014

Status

approved