A204647 Number of (n+1) X 5 0..1 arrays with column and row pair sums b(i,j)=a(i,j)+a(i,j-1) and c(i,j)=a(i,j)+a(i-1,j) nondecreasing in column and row directions, respectively.

48, 90, 178, 330, 571, 938, 1478, 2248, 3317, 4766, 6690, 9198, 12415, 16482, 21558, 27820, 35465, 44710, 55794, 68978, 84547, 102810, 124102, 148784, 177245, 209902, 247202, 289622, 337671, 391890, 452854, 521172, 597489, 682486, 776882, 881434

Offset

1,1

Comments

Column 4 of A204651.

Links

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

Formula

Empirical: a(n) = 5*a(n-1) -9*a(n-2) +5*a(n-3) +5*a(n-4) -9*a(n-5) +5*a(n-6) -a(n-7) for n>9.

Conjectures from Colin Barker, Jun 08 2018: (Start)

G.f.: x*(48 - 150*x + 160*x^2 + 10*x^3 - 167*x^4 + 145*x^5 - 43*x^6 - 5*x^7 + 4*x^8) / ((1 - x)^6*(1 + x)).

a(n) = (1920 + 9776*n + 3480*n^2 + 540*n^3 + 90*n^4 + 4*n^5)/480 for n>2 and even.

a(n) = (1950 + 9776*n + 3480*n^2 + 540*n^3 + 90*n^4 + 4*n^5)/480 for n>2 and odd.

(End)

Example

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

Crossrefs

Cf. A204651.

Sequence in context: A260099 A224546 A247720 * A260980 A260070 A260973

Adjacent sequences: A204644 A204645 A204646 * A204648 A204649 A204650

Keyword

nonn

Author

R. H. Hardin, Jan 17 2012

Status

approved