A187077 Number of row-convex polyplets with n cells.

1, 4, 18, 83, 385, 1788, 8305, 38575, 179170, 832189, 3865253, 17952864, 83385309, 387298083, 1798875698, 8355202169, 38807241321, 180247221864, 837190686169, 3888482927823, 18060759310562, 83886449530197, 389625723579965

Offset

1,2

Comments

Equivalent to a sequence of row-convex polyhexes (A059716).

Links

Table of n, a(n) for n=1..23.

Formula

G.f.: -((x(x-1)^3)/(1-7x+13x^2-10x^3+2x^4)).

a(n) = 7a(n-1)-13a(n-2)+10a(n-3)-2a(n-4) for n > 4.

Example

a(3) = 18 = A006770(3)-2 omits the two 3-plets with non-convex rows (V and inverted V).

Mathematica

a[n_]:={1, 4, 18, 83}[[n]]/; n<5; a[n_]:=a[n]=7a[n-1]-13a[n-2]+10a[n-3]-2a[n-4]; Array[a, 23]

Crossrefs

Cf. A006770 (all fixed polyplets); A059716 (row-convex polyhexes); A001169 (row-convex polyominoes).

Sequence in context: A052913 A279285 A129160 * A218986 A143646 A290916

Adjacent sequences: A187074 A187075 A187076 * A187078 A187079 A187080

Keyword

nonn

Author

David Bevan, Mar 03 2011

Status

approved