A222763 Number of nX2 0..1 arrays with exactly floor(nX2/2) elements unequal to at least one horizontal or antidiagonal neighbor, with new values introduced in row major 0..1 order

0, 3, 4, 20, 48, 175, 512, 1719, 5400, 17776, 57420, 188656, 617176, 2033175, 6697744, 22139780, 73262232, 242931321, 806516560, 2681475048, 8925158440, 29740390672, 99196158144, 331163178475, 1106489052968, 3699881730900, 12380449027324

Offset

1,2

Comments

From Gus Wiseman, Oct 05 2022: (Start)

Conjecture: Also the number of integer compositions of 2n + 1 with the same length as reverse-alternating sum. Here, the reverse-alternating sum of a sequence (y_1,...,y_k) is Sum_i (-1)^i y_i. For example, the a(4) = 20 compositions are:

(135) (234) (333) (432) (531)

(11115) (21114) (31113) (41112) (51111)

(11214) (21213) (31212) (41211)

(11313) (21312) (31311)

(11412) (21411)

(11511)

This is the odd-indexed version of A357182, and the corresponding unordered count (partitions) is A357488.

(End)

Links

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

Example

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

Crossrefs

Column k = 2 of A222769.

Sequence in context: A262033 A062870 A226964 * A306668 A300499 A151419

Adjacent sequences: A222760 A222761 A222762 * A222764 A222765 A222766

Keyword

nonn

Author

R. H. Hardin Mar 05 2013

Status

approved