A196423 Number of n X 1 0..4 arrays with each element equal to the number its horizontal and vertical neighbors less than itself.

1, 3, 5, 11, 26, 55, 119, 263, 573, 1248, 2729, 5959, 13005, 28399, 62010, 135383, 295595, 645407, 1409161, 3076736, 6717713, 14667339, 32024421, 69921635, 152665786, 333328023, 727783135, 1589030151, 3469463141, 7575170720

Offset

1,2

Comments

Column 1 of A196430.

Links

R. H. Hardin, Table of n, a(n) for n = 1..200

Portia X. Anderson, Esther Banaian, Melanie J. Ferreri, Owen C. Goff, Kimberly P. Hadaway, Pamela E. Harris, Kimberly J. Harry, Nicholas Mayers, Shiyun Wang, and Alexander N. Wilson, The support of Kostant's weight multiplicity formula is an order ideal in the weak Bruhat order, arXiv:2412.16820 [math.RT], 2024. See p. 21.

Formula

Empirical: a(n) = a(n-1) +a(n-2) +3*a(n-3) +a(n-4).

Empirical: G.f. -x*(1+x)^2 / ( -1+x+x^2+3*x^3+x^4 ). - R. J. Mathar, Jul 25 2012

Example

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

Crossrefs

Cf. A196430.

Sequence in context: A027050 A240148 A109249 * A320177 A289468 A289534

Adjacent sequences: A196420 A196421 A196422 * A196424 A196425 A196426

Keyword

nonn

Author

R. H. Hardin, Oct 02 2011

Status

approved