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Search: id:A049037
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| A049037 |
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Number of cubic lattice walks that start and end at origin after 2n steps, not touching origin at intermediate stages. |
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4
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| 1, 6, 54, 996, 22734, 577692, 15680628, 445162392, 13055851998, 392475442092, 12029082873372, 374482032292008, 11808861461931492, 376406128925067528, 12108063535794336312, 392560994063887113744, 12814685828476778001726
(list; graph; listen)
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OFFSET
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0,2
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REFERENCES
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S. R. Finch, Mathematical Constants, Cambridge, 2003, pp. 322-331.
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LINKS
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S. R. Finch, Symmetric Random Walk on n-Dimensional Integer Lattice
N. J. A. Sloane, Transforms
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FORMULA
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Define a_0, a_1, ... = [ 1, 6, 54, ... ] by 1+Sum b_i x^i = 1/(1-Sum a_i x^i) where b_0, b_1, ... = [ 1, 6, 90, ... ] = A002896.
Or, Sum[ a(n) x^(2n), n=1, 2, ...infinity ] = 1-1/Sum[ A002896(n)*x^(2n), n=0, 1, ...infinity ].
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EXAMPLE
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a(5)=577692 i.e. there are 577692 different walks that start and end at origin after 2*5=10 steps, avoiding origin at intermediate steps.
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MAPLE
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read transforms; t1 := [ seq(A002896(i), i=1..25) ]; INVERTi(t1);
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CROSSREFS
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Invert A002896.
Sequence in context: A137591 A072034 A138434 this_sequence A047681 A075575 A073655
Adjacent sequences: A049034 A049035 A049036 this_sequence A049038 A049039 A049040
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KEYWORD
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easy,nonn,nice
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AUTHOR
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Alessandro Zinani (alzinani(AT)tin.it)
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