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Search: id:A038201
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| 1, 1, 1, 1, 1, 2, 3, 4, 5, 9, 12, 14, 15, 29, 41, 50, 55, 105, 146, 175, 190, 365, 511, 616, 671, 1287, 1798, 2163, 2353, 4516, 6314, 7601, 8272, 15873, 22187, 26703, 29056, 55759, 77946, 93819, 102091, 195910, 273856, 329615, 358671, 688286, 962142
(list; graph; listen)
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OFFSET
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0,6
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COMMENT
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a(4n) forms A006358. A second recurrence formula is: a(n)=3a(n-4)+3a(n-8)-4a(n-12)-a(n-16)+a(n-20).
Sequence of perfect distributions for a cascade merge with six tapes according to Knuth. - Michael Somos Feb 07 2004
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REFERENCES
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D. E. Knuth, Art of Computer Programming, Vol. 3, Sect. 5.4.3, Eq. (1).
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LINKS
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F. v. Lamoen, Wave sequences
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FORMULA
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a(n)=a(n-1)+a(n-2) if n=4m+1, a(n)=a(n-1)+a(n-4) if n=4m+2, a(n)=a(n-1)+a(n-6) if n=4m+3 and a(n)=a(n-1)+a(n-8) if n=4m.
G.f.: -(1+x+x^2+x^3-2*x^4-x^5+x^7-x^8-x^11+x^12)/(-1+3*x^4+3*x^8-4*x^12-x^16+x^20)
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PROGRAM
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(PARI) a(n)=local(m); if(n<=0, n==0, m=(n-1)\4*4; sum(k=2*m-n, m, a(k)))
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CROSSREFS
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Cf. A038196, A038197.
Sequence in context: A093305 A065817 A084542 this_sequence A033084 A076134 A101526
Adjacent sequences: A038198 A038199 A038200 this_sequence A038202 A038203 A038204
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KEYWORD
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easy,nonn
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AUTHOR
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Floor van Lamoen (fvlamoen(AT)hotmail.com)
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EXTENSIONS
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Edited by Floor van Lamoen (fvlamoen(AT)hotmail.com), Feb 05 2002
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