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Search: id:A051049
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| A051049 |
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Number of moves needed to solve an n-ring baguenaudier if the two end rings can be moved simultaneously. |
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4
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| 1, 1, 4, 7, 16, 31, 64, 127, 256, 511, 1024, 2047, 4096, 8191, 16384, 32767, 65536, 131071, 262144, 524287, 1048576, 2097151, 4194304, 8388607, 16777216, 33554431, 67108864, 134217727, 268435456, 536870911, 1073741824
(list; graph; listen)
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OFFSET
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0,3
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LINKS
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Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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FORMULA
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a(n)=(2^(n+1)-(1+(-1)^(n+1)))/2. - Paul Barry (pbarry(AT)wit.ie), Apr 24 2003
a(n+2)=a(n+1)+2a(n)+1, a(0)=a(1)=1 - Paul Barry (pbarry(AT)wit.ie), May 01 2003
a(n)= (sum{k=0..n, 2^k}+(-1)^n)/2=(A000225(n+1)+(-1)^n)/2. - Paul Barry (pbarry(AT)wit.ie), May 27 2003
(a(n+1)-a(n))/3=A001045(n) - Paul Barry (pbarry(AT)wit.ie), May 27 2003
a(n)=sum{k=0..floor(n/2), C(n+1, 2k) } - Paul Barry (pbarry(AT)wit.ie), May 27 2003
a(n)=sum{k=0..n, C(n, k)+(-1)^(n-k)}-1 - Paul Barry (pbarry(AT)wit.ie), Jul 21 2003
G.f.:(1-x+x^2)/((1-x^2)(1-2x)); E.g.f.: exp(2x)-sinh(x). - Paul Barry (pbarry(AT)wit.ie), Sep 19 2003
a(n)=sum{k=0..n, sum{j=0..n-k, if(mod(j-k, 2)=0, binomial(n-k, j), 0}}; - Paul Barry (pbarry(AT)wit.ie), Jan 25 2005
Row sums of triangle A135221 - Gary W. Adamson (qntmpkt(AT)yahoo.com), Nov 23 2007
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MATHEMATICA
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b[n_?EvenQ] := 2^(n - 1) - 1; b[n_?OddQ] := 2^(n - 1); Table[b[n], {n, 50}]]
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CROSSREFS
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Cf. A000975. Row sums of A131086.
Cf. A135221.
Sequence in context: A025619 A093210 A133600 this_sequence A108122 A027609 A050357
Adjacent sequences: A051046 A051047 A051048 this_sequence A051050 A051051 A051052
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KEYWORD
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nonn
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AUTHOR
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Eric Weisstein (eric(AT)weisstein.com)
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