|
|
A124999
|
|
Number of base 5 circular n-digit numbers with adjacent digits differing by 3 or less.
|
|
2
|
|
|
1, 5, 23, 101, 467, 2165, 10055, 46709, 216995, 1008101, 4683383, 21757829, 101081459, 469599317, 2181641639, 10135364501, 47086382915, 218751625157, 1016265649367, 4721317472933, 21934066839827, 101900219778101, 473403079631879, 2199312977861813
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
[Empirical] a(base,n)=a(base-1,n)+A025012(n+1) for base>=3.int(n/2)+1
|
|
LINKS
|
|
|
FORMULA
|
G.f.: (1 - 2*x)*(1 + 2*x + 3*x^2) / ((1 - x)*(1 - 4*x - 3*x^2)).
a(n) = 1 + (2-sqrt(7))^n + (2+sqrt(7))^n for n>0.
a(n) = 5*a(n-1) - a(n-2) - 3*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]`-$[(i+1)mod N]`>3)+($[(i+1)mod N]`-$[i]`>3))
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,base
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|