A099048 Number of 5 X n 0-1 matrices avoiding simultaneously the right angled numbered polyomino patterns (ranpp) (00;1), (01;0), (10;0) and (11;0).

32, 50, 68, 86, 104, 122, 140, 158, 176, 194, 212, 230, 248, 266, 284, 302, 320, 338, 356, 374, 392, 410, 428, 446, 464, 482, 500, 518, 536, 554, 572, 590, 608, 626, 644, 662, 680, 698, 716, 734, 752, 770, 788, 806, 824, 842, 860, 878, 896, 914, 932, 950, 968, 986

Offset: 1

Author

Sergey Kitaev, Nov 13 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 i1

Also, temperatures in Fahrenheit that convert to Celsius as nonnegative multiples of 10. - J. Lowell, Jul 28 2007

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..5000
• 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. A017245.

Programs

Magma

[18*n+14: n in [1..60]]; // Vincenzo Librandi, Jul 25 2011

Mathematica

Table[18n + 14, {n, 52}] (* Robert G. Wilson v, Nov 16 2004 *)

Formula

a(n) = 18*n + 14.

a(n) = 2*A017245(n).

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

G.f.: 2*x*(16-7*x)/(1-x)^2.

E.g.f.: 2*(exp(x)*(9*x + 7) - 7).

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

Extensions

More terms from Robert G. Wilson v, Nov 16 2004

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