0,1

Number of 5 X n 0-1 matrices avoiding simultaneously the right angled numbered polyomino patterns (ranpp) (00;1), (01;0), (11;0) and (01;1). 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<i2, j1<j2 and these elements are in the same relative order as those in the triple (x,y,z). In general, the number of m x n 0-1 matrices in question is given by 2^m+2m(n-1). Cf. m=2: A008574; m=3: A016933; m=4: A022144; m=6: A017569. - Sergey Kitaev (kitaev(AT)ms.uky.edu), Nov 13 2004

For many of these numbers n (12, 22, 42, 52, 62, 92,..etc), (n^2+1)/5 is prime [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Jan 09 2009]

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.

(Other) sage: [i+2 for i in range(442) if gcd(i, 10) == 10] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 20 2009]

Subsequence of A034709, together with A017281, A139222, A139245, A017329, A139249, A139264, A139279 and A139280.

Sequence in context: A077410 A063599 A163479 this_sequence A120672 A108960 A111095

Adjacent sequences: A017290 A017291 A017292 this_sequence A017294 A017295 A017296

nonn,easy

N. J. A. Sloane (njas(AT)research.att.com).