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Search: id:A092896
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| A092896 |
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Related to random walks on the 4-cube. |
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+0
3
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| 1, 1, 5, 17, 65, 257, 1025, 4097, 16385, 65537, 262145, 1048577, 4194305, 16777217, 67108865, 268435457, 1073741825, 4294967297, 17179869185, 68719476737, 274877906945, 1099511627777, 4398046511105, 17592186044417, 70368744177665
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Gives the denominators in the probability that a random walk on the 4-cube returns to its starting corner on the 2n-th step. Partial sums of A092898. Binomial transform of A092897.
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REFERENCES
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M. Kac. Random walk and the theory of Brownian motion. Amer. Math. Monthly, 54:369-391, 1947
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FORMULA
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G.f.: (1-4x+4x^2-4x^3)/((1-x)(1-4x)); a(n)=1+4^n/4-0^n/4+sum{k=0..n, binom(n, k)*k*(-1)^k}.
a(n+1)=4^n+1-0^n=A002450(n+1)-4*A002450(n-1); - Paul Barry (pbarry(AT)wit.ie), Mar 13 2008
a(n)=A052539(n-1), n>1. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 08 2008]
Dropping a(0) and interleaving the terms with zeros gives a sequence with e.g.f. [sin(5ix/2)/sin(ix/2) - 3]/2 = cos(2ix) + cos(ix) - 1 . Similar expressions apply to A091775 and A074515, which are also power sums representable by the Bernoulli polynomials. [From Tom Copeland (tcjpn(AT)msn.com), Oct 22 2008]
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CROSSREFS
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Cf. A066443.
Sequence in context: A149672 A149673 A046231 this_sequence A149674 A149675 A149676
Adjacent sequences: A092893 A092894 A092895 this_sequence A092897 A092898 A092899
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KEYWORD
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easy,nonn
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Mar 12 2004
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