

A126362


Number of base 8 ndigit numbers with adjacent digits differing by one or less.


8



1, 8, 22, 62, 176, 502, 1436, 4116, 11814, 33942, 97582, 280676, 807574, 2324116, 6689624, 19257202, 55439298, 159611886, 459545688, 1323132230, 3809653732, 10969153364, 31583803574, 90940708414, 261850874726, 753964626300
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,2


COMMENTS

[Empirical] a(base,n) = a(base1,n) + 3^(n1) for base >= n; a(base,n) = a(base1,n) + 3^(n1)2 when base=n1.


LINKS



FORMULA

Conjecture: a(n) = 5*a(n1)  6*a(n2)  a(n3) + 2*a(n4) for n > 4.
G.f.: (4*x^4 + x^3  12*x^2 + 3*x + 1)/((2*x  1)*(x^3  3*x + 1)). (End)
a(n) = e^T A^(n1) e for n>=1, where A is the 8 X 8 matrix with 1 on the main diagonal and first super and subdiagonals, 0 elsewhere, and e the column vector (1,1,1,1,1,1,1,1). Barker's conjecture follows from the fact that (A^4  5*A^3 + 6*A^2 + A  2*I)*e = 0. (End)


MAPLE

f:= gfun:rectoproc({a(n)=5*a(n1)6*a(n2)a(n3)+2*a(n4), a(0)=1, a(1)=8, a(2)=22, a(3)=62, a(4)=176}, a(n), remember):


PROG

(S/R) stvar $[N]:(0..M1) init $[]:=0 asgn $[]>{*} kill +[i in 0..N2](($[i]`$[i+1]`>1)+($[i+1]`$[i]`>1))


CROSSREFS



KEYWORD

nonn,base


AUTHOR



STATUS

approved



