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A126505
Number of base 10 n-digit numbers with adjacent digits differing by four or less.
1
1, 10, 70, 510, 3720, 27142, 198034, 1444904, 10542368, 76919662, 561224422, 4094828862, 29876859864, 217988781808, 1590498774316, 11604663002012, 84670422615182, 617775842744470, 4507441679052256, 32887382581680414
OFFSET
0,2
COMMENTS
[Empirical] a(base,n)=a(base-1,n)+9^(n-1) for base>=4n-3; a(base,n)=a(base-1,n)+9^(n-1)-2 when base=4n-4.
FORMULA
Conjectures from Colin Barker, May 31 2017: (Start)
G.f.: (1 + 3*x - 3*x^2 - 4*x^3 + x^4 + x^5) / (1 - 7*x - 3*x^2 + 6*x^3 + x^4 - x^5).
a(n) = 7*a(n-1) + 3*a(n-2) - 6*a(n-3) - a(n-4) + a(n-5) for n>5.
(End)
PROG
(S/R) stvar $[N]:(0..M-1) init $[]:=0 asgn $[]->{*} kill +[i in 0..N-2](($[i]`-$[i+1]`>4)+($[i+1]`-$[i]`>4))
CROSSREFS
Base 10 differing by three or less A126478, two or less A126397, one or less A126364.
Sequence in context: A257114 A037600 A037705 * A038779 A246427 A172499
KEYWORD
nonn,base
AUTHOR
R. H. Hardin, Dec 28 2006
STATUS
approved