A250438 Number of (n+1)X(3+1) 0..2 arrays with nondecreasing sum of every two consecutive values in every row and column.
1296, 14400, 160000, 1000000, 6250000, 27562500, 121550625, 423536400, 1475789056, 4337012736, 12745506816, 32920473600, 85030560000, 198470250000, 463250390625, 996503062500, 2143588810000, 4311270849600, 8670998958336
Offset: 1
Keywords
Examples
Some solutions for n=3 ..0..1..0..1....0..0..1..1....0..0..0..2....0..0..1..0....0..0..0..1 ..1..2..2..2....0..0..0..0....1..2..2..2....1..0..2..1....0..1..2..2 ..0..1..0..1....0..1..2..2....2..2..2..2....0..2..2..2....1..0..2..2 ..2..2..2..2....0..0..1..1....2..2..2..2....1..1..2..1....0..1..2..2
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) = (1/1358954496)*n^16 + (5/84934656)*n^15 + (31/14155776)*n^14 + (2135/42467328)*n^13 + (33847/42467328)*n^12 + (32735/3538944)*n^11 + (431429/5308416)*n^10 + (1463225/2654208)*n^9 + (5160755/1769472)*n^8 + (8008825/663552)*n^7 + (12913699/331776)*n^6 + (6965/72)*n^5 + (139417/768)*n^4 + (23855/96)*n^3 + (3741/16)*n^2 + 135*n + 36
Empirical for n mod 2 = 1: a(n) = (1/1358954496)*n^16 + (5/84934656)*n^15 + (373/169869312)*n^14 + (1435/28311552)*n^13 + (275299/339738624)*n^12 + (807985/84934656)*n^11 + (14409143/169869312)*n^10 + (49767325/84934656)*n^9 + (2153003003/679477248)*n^8 + (380990005/28311552)*n^7 + (7598369275/169869312)*n^6 + (9778683875/84934656)*n^5 + (76415846875/339738624)*n^4 + (9127365625/28311552)*n^3 + (2011296875/6291456)*n^2 + (616328125/3145728)*n + (937890625/16777216)
Comments