OFFSET
0,1
COMMENTS
Number of 4 X n binary matrices avoiding simultaneously the right angled numbered polyomino patterns (ranpp) (00;1), (01;0), (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 same relative order as those in the triple (x,y,z). - Sergey Kitaev, Nov 11 2004
Numbers k such that k and (4^h)^k end with the same digit, where h > 0. - Bruno Berselli, Dec 13 2018
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..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.
S. Kitaev, On multi-avoidance of right angled numbered polyomino patterns, University of Kentucky Research Reports (2004).
Index entries for linear recurrences with constant coefficients, signature (2,-1).
FORMULA
a(n) = 2*a(n-1) - a(n-2) with n>1, a(0)=6, a(1)=16. - Vincenzo Librandi, May 29 2011
From Stefano Spezia, May 31 2021: (Start)
G.f.: 2*(3 + 2*x)/(1 - x)^2.
E.g.f.: 2*(3 + 5*x)*exp(x). (End)
MATHEMATICA
Range[6, 1000, 10] (* Vladimir Joseph Stephan Orlovsky, May 28 2011 *)
PROG
(Magma) [10*n+6: n in [0..60]]; // Vincenzo Librandi, May 29 2011
(PARI) a(n)=10*n+6 \\ Charles R Greathouse IV, Jul 10 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved