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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 From Colin Barker, Nov 26 2012: (Start) 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)). (End) 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 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(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 December 2 20:20 EST 2023. Contains 367526 sequences. (Running on oeis4.)