0,2

Number of 3 X n 0-1 matrices avoiding simultaneously the right angled numbered polyomino patterns (ranpp) (00;1), (10;0) and (11;0). 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+n)-2^m-2^n+2. - Sergey Kitev (kitaev(AT)ms.uky.edu), Nov 13 2004

Row sums of triangle A131115.

S. Kitaev, On multi-avoidance of right angled numbered polyomino patterns, Integers: Electronic Journal of Combinatorial Number Theory 4 (2004), A21, 20pp.

Equals binomial transform of [1, 7, 7, 7,...] - Gary W. Adamson (qntmpkt(AT)yahoo.com), Apr 28 2008

a(n) = A000079(n)*7-6 = A005009(n)-6. [From Omar E. Pol (info(AT)polprimos.com), Dec 21 2008]

a[n_]:=7*2^n-6; ...and/or...a=1; lst={}; k=7; Do[a+=k; AppendTo[lst, a]; k+=k, {n, 0, 5!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Dec 16 2008]

a(n)=T(6, n), array T given by A048483.

n-th difference of a(n), a(n-1), ..., a(0) is (7, 7, 7, ...).

Cf. A131115.

Cf. A000079, A005009. [From Omar E. Pol (info(AT)polprimos.com), Dec 21 2008]

Sequence in context: A069099 A145067 A112684 this_sequence A124701 A002968 A058404

Adjacent sequences: A048486 A048487 A048488 this_sequence A048490 A048491 A048492

nonn

Clark Kimberling (ck6(AT)evansville.edu)