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A126378
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Number of base 24 n-digit numbers with adjacent digits differing by one or less.
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5
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1, 24, 70, 206, 608, 1798, 5324, 15780, 46806, 138918, 412508, 1225432, 3641690, 10825628, 32190154, 95741294, 284820048, 847475910, 2522096172, 7507000776, 22347852666, 66537181776, 198128815230, 590039959434, 1757365514652
(list;
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listen;
history;
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internal format)
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OFFSET
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0,2
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COMMENTS
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[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
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LINKS
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FORMULA
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G.f.: -(7*x^12 +92*x^11 -206*x^10 -680*x^9 +1145*x^8 +946*x^7 -2100*x^6 +318*x^5 +1050*x^4 -725*x^3 +176*x^2 -11*x -1) / ((x^2 -3*x +1)*(x^10 +15*x^9 +10*x^8 -65*x^7 -10*x^6 +97*x^5 -35*x^4 -40*x^3 +35*x^2 -10*x +1)). - Alois P. Heinz, Sep 25 2015
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MAPLE
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b:= proc(n, i) option remember; `if`(n=0, 1, add(
`if`(i=0 or abs(i-j)<2, b(n-1, j), 0), j=1..24))
end:
a:= n-> b(n, 0):
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PROG
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(S/R) stvar $[N]:(0..M-1) init $[]:=0 asgn $[]->{*} kill +[i in 0..N-2](($[i]`-$[i+1]`>1)+($[i+1]`-$[i]`>1))
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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