A099943 Number of 5 X n binary matrices avoiding simultaneously the right angled numbered polyomino patterns (ranpp) (00;1), (01,1) and (11;0).

72, 98, 124, 150, 176, 202, 228, 254, 280, 306, 332, 358, 384, 410, 436, 462, 488, 514, 540, 566, 592, 618, 644, 670, 696, 722, 748, 774, 800, 826, 852, 878, 904, 930, 956, 982, 1008, 1034, 1060, 1086, 1112, 1138, 1164, 1190, 1216, 1242, 1268, 1294, 1320

Offset: 2

Author

Sergey Kitaev, Nov 12 2004

Keywords

• nonn
• easy

Comments

An occurrence of a ranpp (xy;z) in a matrix A=(a(i,j)) is a triple (a(i1,j1), a(i1,j2), a(i2,j1)) where i11 and n>1.

Links

• Tanya Khovanova, Recursive Sequences.
• S. Kitaev, On multi-avoidance of right angled numbered polyomino patterns, Integers: Electronic Journal of Combinatorial Number Theory 4 (2004), A21, 20pp.
• Index entries for linear recurrences with constant coefficients, signature (2,-1).

Crossrefs

Cf. A016957 (m=2), A008592 (m=3), A063130 (m=4).

Cf. A252994.

Programs

Mathematica

Range[72, 7000, 26] (* Vladimir Joseph Stephan Orlovsky, Jul 13 2011 *)

Formula

a(n) = 26*n + 20.

From Elmo R. Oliveira, Jul 01 2025: (Start)

G.f.: 2*x^2*(36-23*x)/(1-x)^2.

E.g.f.: 2*(exp(x)*(10 + 13*x) - (10 + 23*x)).

a(n) = 2*a(n-1) - a(n-2) for n > 3.

a(n) = A252994(n) + 20. (End)