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A204646 Number of (n+1) X 4 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. 1
28, 56, 104, 178, 284, 434, 637, 908, 1259, 1708, 2270, 2966, 3814, 4838, 6059, 7504, 9197, 11168, 13444, 16058, 19040, 22426, 26249, 30548, 35359, 40724, 46682, 53278, 60554, 68558, 77335, 86936, 97409, 108808, 121184, 134594, 149092, 164738, 181589 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Column 3 of A204651.
LINKS
FORMULA
Empirical: a(n) = 4*a(n-1) -5*a(n-2) +5*a(n-4) -4*a(n-5) +a(n-6) for n>7.
Conjectures from Colin Barker, Jun 08 2018: (Start)
G.f.: x*(28 - 56*x + 20*x^2 + 42*x^3 - 48*x^4 + 20*x^5 - 3*x^6) / ((1 - x)^5*(1 + x)).
a(n) = (256 + 400*n + 144*n^2 + 16*n^3 + 2*n^4)/32 for n>1 and even.
a(n) = (238 + 400*n + 144*n^2 + 16*n^3 + 2*n^4)/32 for n>1 and odd.
(End)
EXAMPLE
Some solutions for n=5:
..0..0..0..1....0..0..0..1....0..0..0..0....0..0..0..0....0..0..0..0
..1..1..1..1....0..0..0..1....0..0..1..1....0..0..0..1....0..0..0..0
..1..1..1..1....0..0..0..1....1..1..1..1....0..0..0..1....0..0..0..0
..1..1..1..1....0..0..1..1....1..1..1..1....0..0..0..1....0..0..0..1
..1..1..1..1....0..1..1..1....1..1..1..1....0..0..1..1....0..0..0..1
..1..1..1..1....1..1..1..1....1..1..1..1....0..0..1..1....1..1..1..1
CROSSREFS
Cf. A204651.
Sequence in context: A119168 A040756 A135628 * A211491 A270297 A068576
KEYWORD
nonn
AUTHOR
R. H. Hardin, Jan 17 2012
STATUS
approved

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Last modified June 22 21:17 EDT 2024. Contains 373609 sequences. (Running on oeis4.)