A048489 a(n) = 7 * 2^n - 6.

1, 8, 22, 50, 106, 218, 442, 890, 1786, 3578, 7162, 14330, 28666, 57338, 114682, 229370, 458746, 917498, 1835002, 3670010, 7340026, 14680058, 29360122, 58720250, 117440506, 234881018, 469762042, 939524090, 1879048186

Offset: 0

Author

Clark Kimberling

Keywords

• nonn
• easy
• nice

Comments

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 i1Sergey Kitev, Nov 13 2004

Row sums of triangle A131115. - N. J. A. Sloane, Nov 10 2007

Equals binomial transform of [1, 7, 7, 7, ...]. - Gary W. Adamson, Apr 28 2008

Number of variations of a Componium barrel which produces n phrases. This sequence describes the variations produced by the Componium, a historical mechanical organ. Another way of describing it is: Number of base 8 n-digit numbers produced by repeating or advancing along this 14-step cycle: (0,1,2,3,4,5,6,7,6,5,4,3,2,1). Subset of A126362. - Jim Bumgardner, Dec 10 2013

a(n) = the sum of the terms in row(n) in a triangle with first column T(n,0)=

1+2*n and diagonal T(n,n)=1+4*n with T(i,j)=T(i-1,j-1) + T(i-1,j). - J. M. Bergot, May 11 2018

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Jim Bumgardner, Variations of the Componium, 2013
• 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 (3,-2).

Crossrefs

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.

Programs

Maple

A048489:=n->7*2^n-6: seq(A048489(n), n=0..40); # Wesley Ivan Hurt, Apr 18 2017

Mathematica

CoefficientList[Series[(1 + 5 x)/((2 x - 1) (x - 1)), {x, 0, 28}], x] (* Michael De Vlieger, May 22 2018 *)
7*2^Range[0,30]-6 (* or *) LinearRecurrence[{3,-2},{1,8},30] (* Harvey P. Dale, May 19 2019 *)

PARI

a(n)=7<Charles R Greathouse IV, Dec 10 2013

Formula

a(n) = A000079(n)*7-6 = A005009(n)-6. - Omar E. Pol, Dec 21 2008

a(n) = 2*a(n-1)+6 with n>0, a(0)=1. - Vincenzo Librandi, Aug 06 2010

G.f.: ( 1+5*x ) / ( (2*x-1)*(x-1) ). - R. J. Mathar, Oct 21 2012

a(n) = A063757(2*n). - Philippe Deléham, Apr 13 2013