A250440 Number of (n+1)X(5+1) 0..2 arrays with nondecreasing sum of every two consecutive values in every row and column.
10000, 250000, 6250000, 76562500, 937890625, 7353062500, 57648010000, 332052537600, 1912622616576, 8782450790400, 40327580160000, 155600676000000, 600372506250000, 2017918701562500, 6782448969140625, 20377491125062500
Offset: 1
Keywords
Examples
Some solutions for n=1 ..0..1..1..1..2..2....2..0..2..0..2..0....1..2..1..2..1..2....0..0..0..1..0..1 ..0..0..2..1..2..1....0..1..1..1..1..1....0..1..0..1..1..2....0..0..0..2..2..2
Links
- R. H. Hardin, Table of n, a(n) for n = 1..210
Formula
Empirical: a(n) = 2*a(n-1) +22*a(n-2) -46*a(n-3) -230*a(n-4) +506*a(n-5) +1518*a(n-6) -3542*a(n-7) -7084*a(n-8) +17710*a(n-9) +24794*a(n-10) -67298*a(n-11) -67298*a(n-12) +201894*a(n-13) +144210*a(n-14) -490314*a(n-15) -245157*a(n-16) +980628*a(n-17) +326876*a(n-18) -1634380*a(n-19) -326876*a(n-20) +2288132*a(n-21) +208012*a(n-22) -2704156*a(n-23) +2704156*a(n-25) -208012*a(n-26) -2288132*a(n-27) +326876*a(n-28) +1634380*a(n-29) -326876*a(n-30) -980628*a(n-31) +245157*a(n-32) +490314*a(n-33) -144210*a(n-34) -201894*a(n-35) +67298*a(n-36) +67298*a(n-37) -24794*a(n-38) -17710*a(n-39) +7084*a(n-40) +3542*a(n-41) -1518*a(n-42) -506*a(n-43) +230*a(n-44) +46*a(n-45) -22*a(n-46) -2*a(n-47) +a(n-48)
Empirical for n mod 2 = 0: a(n) = (1/7213895789838336)*n^24 + (1/50096498540544)*n^23 + (1235/901736973729792)*n^22 + (4477/75144747810816)*n^21 + (831679/450868486864896)*n^20 + (812591/18786186952704)*n^19 + (1405627/1761205026816)*n^18 + (3100741/260919263232)*n^17 + (4094603551/28179280429056)*n^16 + (433465327/293534171136)*n^15 + (44306115959/3522410053632)*n^14 + (26501886041/293534171136)*n^13 + (964685807569/1761205026816)*n^12 + (68759134069/24461180928)*n^11 + (1341490699171/110075314176)*n^10 + (51007464301/1146617856)*n^9 + (935019035443/6879707136)*n^8 + (98748474923/286654464)*n^7 + (34174316941/47775744)*n^6 + (1189590079/995328)*n^5 + (129883723/82944)*n^4 + (41785/27)*n^3 + (156019/144)*n^2 + (1435/3)*n + 100
Empirical for n mod 2 = 1: a(n) = (1/7213895789838336)*n^24 + (1/50096498540544)*n^23 + (2473/1803473947459584)*n^22 + (8987/150289495621632)*n^21 + (6703097/3606947894919168)*n^20 + (6582733/150289495621632)*n^19 + (1467014557/1803473947459584)*n^18 + (203874037/16698832846848)*n^17 + (1087131080383/7213895789838336)*n^16 + (116367833311/75144747810816)*n^15 + (12047121885881/901736973729792)*n^14 + (7311600115943/75144747810816)*n^13 + (1082232553741855/1803473947459584)*n^12 + (78574511484559/25048249270272)*n^11 + (12519441818897777/901736973729792)*n^10 + (3896610583531693/75144747810816)*n^9 + (1172330828707213711/7213895789838336)*n^8 + (63675047896162255/150289495621632)*n^7 + (20207552719915925/22265110462464)*n^6 + (26209033583275375/16698832846848)*n^5 + (95114119934815625/44530220924928)*n^4 + (1361430919121875/618475290624)*n^3 + (443670923390625/274877906944)*n^2 + (51535776796875/68719476736)*n + (182401906640625/1099511627776)
Comments