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A126362 Number of base 8 n-digit 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(base-1,n)+3^(n-1) for base>=n; a(base,n)=a(base-1,n)+3^(n-1)-2 when base=n-1

LINKS

Robert Israel, Table of n, a(n) for n = 0..2174

Jim Bumgardner, Variations of the Componium, 2013

FORMULA

Conjecture: a(n) = 5*a(n-1)-6*a(n-2)-a(n-3)+2*a(n-4) for n>4. G.f.: -(4*x^4+x^3-12*x^2+3*x+1)/((2*x-1)*(x^3-3*x+1)). [Colin Barker, Nov 26 2012]

From Robert Israel, Aug 12 2019: (Start)

a(n) = e^T A^(n-1) e for n>=1, where A is the 8 X 8 matrix with 1 on the main diagonal and first super- and sub-diagonals, 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(n-1)-6*a(n-2)-a(n-3)+2*a(n-4), a(0)=1, a(1)=8, a(2)=22, a(3)=62, a(4)=176}, a(n), remember):

map(f, [$0..30]); # Robert Israel, Aug 12 2019

PROG

(S/R) stvar $[N]:(0..M-1) init $[]:=0 asgn $[]->{*} kill +[i in 0..N-2](($[i]`-$[i+1]`>1)+($[i+1]`-$[i]`>1))

CROSSREFS

Sequence in context: A211479 A318034 A326162 * A140418 A200081 A199110

Adjacent sequences:  A126359 A126360 A126361 * A126363 A126364 A126365

KEYWORD

nonn,base

AUTHOR

R. H. Hardin, Dec 26 2006

STATUS

approved

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Last modified April 7 15:56 EDT 2020. Contains 333306 sequences. (Running on oeis4.)