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

1,1

Comments

Column 7 of A250432.

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

Example

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

Crossrefs

Sequence in context: A171995 A307481 A262798 * A046755 A016816 A046756

Adjacent sequences: A250428 A250429 A250430 * A250432 A250433 A250434

Keyword

nonn

Author

R. H. Hardin, Nov 22 2014

Status

approved