A250431 Number of (n+1)X(7+1) 0..1 arrays with nondecreasing sum of every two consecutive values in every row and column.
625, 5625, 50625, 275625, 1500625, 6002500, 24010000, 77792400, 252047376, 700131600, 1944810000, 4802490000, 11859210000, 26683222500, 60037250625, 125262905625, 261351000625, 512247961225, 1004006004001, 1866953313225
Offset: 1
Keywords
Examples
Some solutions for n=3 ..0..0..0..0..0..0..1..1....1..0..1..0..1..0..1..1....0..0..0..0..1..0..1..0 ..0..1..1..1..1..1..1..1....0..0..1..0..1..0..1..1....1..0..1..0..1..1..1..1 ..1..0..1..0..1..1..1..1....1..0..1..0..1..1..1..1....0..0..0..0..1..1..1..1 ..1..1..1..1..1..1..1..1....1..0..1..1..1..1..1..1....1..1..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) +14*a(n-2) -30*a(n-3) -90*a(n-4) +210*a(n-5) +350*a(n-6) -910*a(n-7) -910*a(n-8) +2730*a(n-9) +1638*a(n-10) -6006*a(n-11) -2002*a(n-12) +10010*a(n-13) +1430*a(n-14) -12870*a(n-15) +12870*a(n-17) -1430*a(n-18) -10010*a(n-19) +2002*a(n-20) +6006*a(n-21) -1638*a(n-22) -2730*a(n-23) +910*a(n-24) +910*a(n-25) -350*a(n-26) -210*a(n-27) +90*a(n-28) +30*a(n-29) -14*a(n-30) -2*a(n-31) +a(n-32)
Empirical for n mod 2 = 0: a(n) = (1/21743271936)*n^16 + (1/226492416)*n^15 + (89/452984832)*n^14 + (203/37748736)*n^13 + (2549/25165824)*n^12 + (1459/1048576)*n^11 + (1224205/84934656)*n^10 + (812447/7077888)*n^9 + (20096035/28311552)*n^8 + (2015611/589824)*n^7 + (3762023/294912)*n^6 + (149513/4096)*n^5 + (26016553/331776)*n^4 + (422071/3456)*n^3 + (12469/96)*n^2 + (505/6)*n + 25
Empirical for n mod 2 = 1: a(n) = (1/21743271936)*n^16 + (1/226492416)*n^15 + (535/2717908992)*n^14 + (1225/226492416)*n^13 + (185693/1811939328)*n^12 + (35725/25165824)*n^11 + (40404433/2717908992)*n^10 + (27184205/226492416)*n^9 + (8206068803/10871635968)*n^8 + (840056675/226492416)*n^7 + (476102705/33554432)*n^6 + (1052064899/25165824)*n^5 + (6239471239/67108864)*n^4 + (1265493285/8388608)*n^3 + (5650169175/33554432)*n^2 + (968932125/8388608)*n + (9845600625/268435456).
a(n+1) = A202098(n). - R. J. Mathar, Dec 02 2014
Comments