A223919 Number of 2 X n 0..2 arrays with rows and antidiagonals unimodal and columns nondecreasing.

6, 36, 158, 548, 1600, 4102, 9503, 20299, 40570, 76704, 138348, 239630, 400700, 649642, 1024813, 1577669, 2376142, 3508636, 5088714, 7260552, 10205240, 14148014, 19366507, 26200111, 35060546, 46443736, 60943096, 79264338

Offset

1,1

Comments

Row 2 of A223918.

Links

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

Formula

Empirical: a(n) = (1/10080)*n^8 + (1/504)*n^7 + (1/40)*n^6 + (109/720)*n^5 + (259/480)*n^4 + (173/144)*n^3 + (4877/2520)*n^2 + (481/420)*n + 1.

Conjectures from Colin Barker, Feb 23 2018: (Start)

G.f.: x*(6 - 18*x + 50*x^2 - 82*x^3 + 88*x^4 - 62*x^5 + 29*x^6 - 8*x^7 + x^8) / (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>9.

(End)

Example

Some solutions for n=3:
..1..2..0....0..0..2....1..0..0....0..0..0....0..1..1....1..2..0....0..1..0
..1..2..0....0..0..2....1..0..0....1..1..0....0..2..1....1..2..2....1..1..2

Crossrefs

Cf. A223918.

Sequence in context: A224149 A055404 A223946 * A263952 A281394 A225380

Adjacent sequences: A223916 A223917 A223918 * A223920 A223921 A223922

Keyword

nonn

Author

R. H. Hardin, Mar 29 2013

Status

approved