|
|
A125343
|
|
Number of base 6 circular n-digit numbers with adjacent digits differing by 4 or less.
|
|
0
|
|
|
1, 6, 34, 186, 1058, 6026, 34354, 195866, 1116738, 6367146, 36302674, 206981946, 1180120418, 6728529866, 38363130994, 218729774426, 1247101396098, 7110426078186, 40540535975314, 231144384189306, 1317884064847778
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
[Empirical] a(base,n)=a(base-1,n)+A025014(n+1) for base>=4.int(n/2)+1
|
|
LINKS
|
|
|
FORMULA
|
G.f.: (1 - x^2 - 8*x^3) / ((1 - x)*(1 - 5*x - 4*x^2)).
a(n) = 1 + ((5-sqrt(41))/2)^n + ((5+sqrt(41))/2)^n for n>0.
a(n) = 6*a(n-1) - a(n-2) - 4*a(n-3) for n>3.
(End)
|
|
PROG
|
(S/R) stvar $[N]:(0..M-1) init $[]:=0 asgn $[]->{*} kill +[i in 0..N-1](($[i]`-$[(i+1)mod N]`>4)+($[(i+1)mod N]`-$[i]`>4))
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,base
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|