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Search: id:A063886
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| A063886 |
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Number of n-step walks on a line starting from the origin but not returning to it. |
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+0
7
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| 1, 2, 2, 4, 6, 12, 20, 40, 70, 140, 252, 504, 924, 1848, 3432, 6864, 12870, 25740, 48620, 97240, 184756, 369512, 705432, 1410864, 2704156, 5408312, 10400600, 20801200, 40116600, 80233200, 155117520, 310235040, 601080390, 1202160780
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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A Chebyshev transform of A007877(n+1). The g.f. is transformed to (1+x)/((1-x)(1+x^2)) under the mapping G(x)->(1/(1+x^2))G(1/(1+x^2)). - Paul Barry (pbarry(AT)wit.ie), Oct 12 2004
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REFERENCES
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D. Perrin, A conjecture on rational sequences, pp. 267-274 of R. M. Capocelli, ed., Sequences, Springer-Verlag, NY 1990.
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FORMULA
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a(n+1) = 2*C(n, [n/2]) = 2*A001405(n); a(2n) = C(2n, n) = A000984(n) = 4*a(2n-2)-|A002420(n)| = 4*a(2n-2)-2*A000108(n-1) = 2*A001700(n-1); a(2n+1) = 2*a(2n) = A028329(n).
G.f.: sqrt((1+2x)/(1-2x)).
a(n)=Sum_{k, 0<=k<=n} abs(A106180(n,k)). - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 06 2006
a(n)=sum{k=0..n, (k+1)binomial(n, (n-k)/2) ( 1-cos((k+1)*pi/2) (1+(-1)^(n-k))/(n+k+2) ) }. - Paul Barry (pbarry(AT)wit.ie), Oct 12 2004
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MAPLE
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seq(seq(binomial(2*j, j)*i, i=1..2), j=0..16); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 28 2007
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PROGRAM
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(PARI) a(n)=(n==0)+2*binomial(n-1, (n-1)\2)
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CROSSREFS
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2a(n)=A047073(n+1).
Cf. A000984.
Adjacent sequences: A063883 A063884 A063885 this_sequence A063887 A063888 A063889
Sequence in context: A059123 A001679 A030435 this_sequence A003000 A122536 A128209
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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), Aug 28 2001
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