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A038196
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3-wave sequence starting with 1, 1, 1.
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12
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1, 1, 1, 2, 3, 5, 6, 11, 14, 25, 31, 56, 70, 126, 157, 283, 353, 636, 793, 1429, 1782, 3211, 4004, 7215, 8997, 16212, 20216, 36428, 45425, 81853, 102069, 183922, 229347, 413269, 515338, 928607, 1157954, 2086561, 2601899, 4688460, 5846414
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| The 3-wave sequence with initial values a, b, c is formed by the following construction:
a.......a+b+c............3a+5b+6c...
..b...b+c...a+2b+2c..2a+4b+5c...
....c..........a+2b+3c...
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REFERENCES
| J. Kappraff, Beyond Measure, World Scientific, Inc. 2002, p. 497.
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LINKS
| F. v. Lamoen, Wave sequences
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FORMULA
| a(n)=a(n-1)+a(n-2) if n is odd, a(n)=a(n-1)+a(n-4) if n is even. Also: a(n)=2a(n-2)+a(n-4)-a(n-6).
G.f.: (1+x-x^2)/(1-2*x^2-x^4+x^6).
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PROG
| (PARI) a(n)=if(n>-1, polcoeff((1+x-x^2)/(1-2*x^2-x^4+x^6)+x*O(x^n), n), if(n<-3, polcoeff((1-x-x^2)/(1-x^2-2*x^4+x^6)+O(x^(-3-n)), -4-n), 0))
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CROSSREFS
| a(2n) forms A006356, a(2n+1)("the middle row") forms A006054. Cf. A038197, A038201, A187070.
Sequence in context: A039844 A187068 A187070 * A039849 A039896 A180336
Adjacent sequences: A038193 A038194 A038195 * A038197 A038198 A038199
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KEYWORD
| easy,nonn
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AUTHOR
| Floor van Lamoen (fvlamoen(AT)hotmail.com)
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EXTENSIONS
| Edited by Floor van Lamoen (fvlamoen(AT)hotmail.com), Feb 05 2002
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