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
Keywords
Examples
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
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
Comments