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Search: id:A102699
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| A102699 |
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Number of different n-digit numbers, using only the digits 1 through n, where consecutive digits differ by 1. |
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+0
1
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| 1, 2, 6, 16, 42, 104, 252, 592, 1370, 3112, 6996, 15536, 34244, 74832, 162616, 351136, 754938, 1615208, 3443940, 7314928, 15493676, 32714992, 68918856, 144815456, 303703972, 635554064, 1327816392, 2769049312, 5766417480, 11989472672, 24897569648, 51632387904, 106958662714, 221305099240, 457456461444, 944605448816, 1948855239068, 4016999161008, 8273530965160, 17026127216608
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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It is assumed that there are n different digits available even when n > 9. - a(20) onwards from David Wasserman (dwasserm(AT)earthlink.net), Apr 26 2008
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FORMULA
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It appears that the limit of a(n)/a(n-1) is decreasing towards 2 - Ben Thurston (benthurston27(AT)yahoo.com), Oct 04 2006
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EXAMPLE
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For example, a(4)=16; the 16 numbers are 1212, 1232, 1234, 2121, 2123, 2321, 2323, 2343, 3212, 3232, 3234, 3432, 3434, 4321, 4323, and 4343.
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MAPLE
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p:= 0; paths := proc(m, n, s, t) global p; if(((t+1) <= m) and s <= (n)) then paths(m, n, s+1, t+1); end if; if(((t-1) > 0) and s <= (n)) then paths(m, n, s+1, t-1); end if; if(s = n) then p:=p+1; end if; end proc; sumpaths:=proc(j) global p; p:=0; sp:=0; for h from 1 to j do p:=0; paths(j, j, 1, h); sp:=sp+ p ; end do; sp; end proc; for l from 1 to 50 do sumpaths(l); end do; - Ben Thurston (benthurston27(AT)yahoo.com), Oct 04 2006
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CROSSREFS
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Adjacent sequences: A102696 A102697 A102698 this_sequence A102700 A102701 A102702
Sequence in context: A074405 A068786 A143123 this_sequence A025169 A111282 A115730
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KEYWORD
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nonn,base
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AUTHOR
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Don Rogers (donrogers42(AT)aol.com), Feb 07 2005
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EXTENSIONS
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More terms from Ben Thurston (benthurston27(AT)yahoo.com), Oct 04 2006
a(20) onwards from David Wasserman (dwasserm(AT)earthlink.net), Apr 26 2008
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