A250429 Number of (n+1)X(5+1) 0..1 arrays with nondecreasing sum of every two consecutive values in every row and column

256, 1600, 10000, 40000, 160000, 490000, 1500625, 3841600, 9834496, 22127616, 49787136, 101606400, 207360000, 392040000, 741200625, 1317690000, 2342560000, 3958926400, 6690585616, 10837642816, 17555190016, 27429984400, 42859350625

Offset

1,1

Comments

Column 5 of A250432.

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

Empirical: a(n) = 2*a(n-1) +10*a(n-2) -22*a(n-3) -44*a(n-4) +110*a(n-5) +110*a(n-6) -330*a(n-7) -165*a(n-8) +660*a(n-9) +132*a(n-10) -924*a(n-11) +924*a(n-13) -132*a(n-14) -660*a(n-15) +165*a(n-16) +330*a(n-17) -110*a(n-18) -110*a(n-19) +44*a(n-20) +22*a(n-21) -10*a(n-22) -2*a(n-23) +a(n-24)

Empirical for n mod 2 = 0: a(n) = (1/5308416)*n^12 + (5/442368)*n^11 + (407/1327104)*n^10 + (275/55296)*n^9 + (5933/110592)*n^8 + (415/1024)*n^7 + (182201/82944)*n^6 + (3715/432)*n^5 + (62483/2592)*n^4 + (2545/54)*n^3 + (731/12)*n^2 + (140/3)*n + 16

Empirical for n mod 2 = 1: a(n) = (1/5308416)*n^12 + (5/442368)*n^11 + (817/2654208)*n^10 + (2225/442368)*n^9 + (97157/1769472)*n^8 + (3455/8192)*n^7 + (3101111/1327104)*n^6 + (2080805/221184)*n^5 + (144963631/5308416)*n^4 + (24654385/442368)*n^3 + (7461475/98304)*n^2 + (3044125/49152)*n + (1500625/65536).

a(n+1) = A202096(n). - R. J. Mathar, Dec 02 2014

Example

Some solutions for n=5
..0..0..0..0..0..0....0..0..0..0..1..1....0..0..0..0..0..1....0..0..0..0..0..1
..0..0..1..1..1..1....0..0..0..0..1..1....0..0..0..0..1..1....0..0..1..0..1..0
..0..0..0..0..0..0....1..0..1..1..1..1....0..0..0..0..0..1....0..0..0..1..1..1
..0..0..1..1..1..1....1..0..1..0..1..1....0..0..0..1..1..1....0..0..1..1..1..1
..0..0..0..1..0..1....1..0..1..1..1..1....0..0..0..1..0..1....1..1..1..1..1..1
..1..0..1..1..1..1....1..1..1..1..1..1....0..0..0..1..1..1....0..0..1..1..1..1

Crossrefs

Sequence in context: A238081 A238074 A251974 * A238155 A238148 A237927

Adjacent sequences: A250426 A250427 A250428 * A250430 A250431 A250432

Keyword

nonn

Author

R. H. Hardin, Nov 22 2014

Status

approved