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Search: id:A068911
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| A068911 |
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Number of n step walks (each step +/-1 starting from 0) which are never more than 2 or less than -2. |
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+0
5
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| 1, 2, 4, 6, 12, 18, 36, 54, 108, 162, 324, 486, 972, 1458, 2916, 4374, 8748, 13122, 26244, 39366, 78732, 118098, 236196, 354294, 708588, 1062882, 2125764, 3188646, 6377292, 9565938, 19131876, 28697814, 57395628, 86093442, 172186884
(list; graph; listen)
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OFFSET
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0,2
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FORMULA
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a(n) =A068913(2, n) =2*A038754(n-1) =3*a(n-2) =a(n-1)*a(n-2)/a(n-3) starting with a(0)=1, a(1)=2, a(2)=4 and a(3)=6. For n>0: a(2n)=4*3^(n-1)=2*a(2n-1); a(2n+1)=2*3^n=3*a(2n)/2=2*a(2n)-A000079(n-2).
G.f.: (1+x)^2/(1-3x^2); a(n)=2*3^((n+1)/2)((1-(-1)^n)/6+sqrt(3)(1+(-1)^n)/9)-0^n/3. The sequence 0, 1, 2, 4, ... has a(n)=2*3^(n/2)((1+(-1)^n)/6+sqrt(3)(1-(-1)^n)/9)-2*0^n/3+sum{k=0..n, binom(n, k)k(-1)^k}/3 - Paul Barry (pbarry(AT)wit.ie), Feb 17 2004
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CROSSREFS
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Cf. A000007, A016116 (without initial term), A068912, A068913 for similar.
A060647(n-1)+1.
Sequence in context: A063516 A104352 A133488 this_sequence A094769 A068018 A060798
Adjacent sequences: A068908 A068909 A068910 this_sequence A068912 A068913 A068914
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KEYWORD
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nonn
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AUTHOR
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Henry Bottomley (se16(AT)btinternet.com), Mar 06 2002
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