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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
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OFFSET
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0,4
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COMMENTS
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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
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J. Kappraff, Beyond Measure, World Scientific, Inc. 2002, p. 497.
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LINKS
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FORMULA
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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) = 2*a(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
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(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
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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