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

Author

Wolfdieter Lang, May 26 2000

Keywords

• easy
• nonn

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).

Crossrefs

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

Programs

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 *)

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]