A055581 Fifth column of triangle A055252.

1, 8, 39, 150, 501, 1524, 4339, 11762, 30705, 77808, 192495, 466926, 1114093, 2621420, 6094827, 14024682, 31981545, 72351720, 162529255, 362807270, 805306341, 1778384868, 3909091299, 8556380130, 18656264161, 40533753824

Offset

0,2

Comments

a(n) = number of directed column-convex polyominoes of area n+5 having along the lower contour exactly two reentrant corners. - Emeric Deutsch, May 21 2003

Links

Michael De Vlieger, Table of n, a(n) for n = 0..3297

Robert Davis, Greg Simay, Further Combinatorics and Applications of Two-Toned Tilings, arXiv:2001.11089 [math.CO], 2020.

A. F. Y. Zhao, Pattern Popularity in Multiply Restricted Permutations, Journal of Integer Sequences, 17 (2014), #14.10.3.

Index entries for linear recurrences with constant coefficients, signature (8, -25, 38, -28, 8).

Formula

G.f.: 1/(((1-2*x)^3)*(1-x)^2).

a(n) = A055252(n+4, 4). a(n) = sum(a(j), j=0..n-1)+A045889(n), n >= 1.

a(n) = (n^2-n+4)2^(n+1)-7-n - Emeric Deutsch, May 21 2003

a(0)=1, a(1)=8, a(2)=39, a(3)=150, a(4)=501, a(n) = 8*a(n-1)- 25*a(n-2)+ 38*a(n-3)-28*a(n-4)+8*a(n-5). [Harvey P. Dale, Nov 07 2011]

Mathematica

Table[(n^2-n+4)2^(n+1)-7-n, {n, 0, 30}] (* or *) LinearRecurrence[ {8, -25, 38, -28, 8}, {1, 8, 39, 150, 501}, 30] (* Harvey P. Dale, Nov 07 2011 *)

Crossrefs

Cf. A055252, A055249, A045889, partial sums of A055580.

Sequence in context: A060446 A318267 A063002 * A297017 A134415 A097787

Adjacent sequences: A055578 A055579 A055580 * A055582 A055583 A055584

Keyword

easy,nonn

Author

Wolfdieter Lang, May 26 2000

Status

approved