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A224160
Number of 4 X n 0..1 arrays with diagonals and rows unimodal and antidiagonals nondecreasing.
1
16, 108, 281, 574, 1156, 2271, 4339, 8008, 14257, 24519, 40840, 66082, 104179, 160456, 242022, 358249, 521350, 747070, 1055505, 1472065, 2028598, 2764693, 3729181, 4981854, 6595423, 8657737, 11274286, 14571012, 18697453, 23830246
OFFSET
1,1
Row 4 of A224158.
FORMULA
Empirical: a(n) = (1/40320)*n^8 - (1/10080)*n^7 + (31/2880)*n^6 + (43/720)*n^5 + (3527/5760)*n^4 - (5947/1440)*n^3 + (548119/10080)*n^2 - (119221/840)*n + 283 for n>4.
Conjectures from Colin Barker, Aug 28 2018: (Start)
G.f.: x*(16 - 36*x - 115*x^2 + 589*x^3 - 950*x^4 + 519*x^5 + 442*x^6 - 977*x^7 + 817*x^8 - 436*x^9 + 178*x^10 - 55*x^11 + 9*x^12) / (1 - x)^9.
a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>13.
(End)
EXAMPLE
Some solutions for n=3:
..1..1..0....1..1..0....1..1..0....0..0..0....1..1..1....0..0..1....0..0..1
..1..1..0....1..1..1....1..1..1....0..0..0....1..1..1....0..1..0....0..1..1
..1..1..0....1..1..1....1..1..0....1..1..0....1..1..1....1..1..1....1..1..0
..1..0..0....1..1..0....1..1..0....1..1..1....1..1..0....1..1..1....1..1..0
CROSSREFS
Cf. A224158.
Sequence in context: A097762 A297610 A083469 * A224411 A260357 A056001
KEYWORD
nonn
AUTHOR
R. H. Hardin, Mar 31 2013
STATUS
approved

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Last modified September 20 02:18 EDT 2024. Contains 376016 sequences. (Running on oeis4.)