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Search: id:A165157
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| 0, 1, 3, 4, 7, 8, 12, 13, 18, 19, 25, 26, 33, 34, 42, 43, 52, 53, 63, 64, 75, 76, 88, 89, 102, 103, 117, 118, 133, 134, 150, 151, 168, 169, 187, 188, 207, 208, 228, 229, 250, 251, 273, 274, 297, 298, 322, 323, 348, 349, 375, 376, 403, 404, 432, 433, 462, 463, 493, 494, 525
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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A133622 is a toothed sequence.
Interleaving of A055998 and A034856.
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FORMULA
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a(0) = 0, a(2n) = a(2n-1) + n + 1, a(2n+1) = a(2n) + 1. a(n) = (n^2 + 10n) / 8 if n is even, a(n) = (n^2 + 8n - 1) / 8 if n is odd. a(2k) = A055998(k) = k * (k+5) / 2 for k >= 0. a(2k+1) = A034856(k+1) = k * (k+5) / 2 + 1 for k >= 0.
a(n) = 2*a(n-2)-a(n-4)+1 for n > 3; a(0)=0, a(1)=1, a(2)=3, a(3)=4. [From Klaus Brockhaus, Sep 06 2009]
(2*n*(n+9)-1+(2*n+1)*(-1)^n)/16. [From Klaus Brockhaus, Sep 06 2009]
G.f.: x*(1+2*x-x^2-x^3)/((1-x)^3*(1+x)^2). [From Klaus Brockhaus, Sep 06 2009]
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PROGRAM
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(MAGMA) m:=60; T:=[ 1+(1+(-1)^n)*n/4: n in [1..m] ]; [0] cat [ n eq 1 select T[1] else Self(n-1)+T[n]: n in [1..m] ]; [From Klaus Brockhaus, Sep 06 2009]
(MAGMA) [ n le 2 select n-1 else n le 4 select n else 2*Self(n-2)-Self(n-4)+1: n in [1..61] ]; [From Klaus Brockhaus, Sep 06 2009]
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CROSSREFS
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Equals -1+A101881.
a(n) = A117142(n+2)-2 = A055802(n+6)-3 = A114220(n+5)-3 = A134519(n+3)-3.
Cf. A133622, A055998, A034856.
Sequence in context: A045615 A051201 A026449 this_sequence A129819 A025032 A003141
Adjacent sequences: A165154 A165155 A165156 this_sequence A165158 A165159 A165160
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KEYWORD
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nonn
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AUTHOR
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Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Sep 05 2009
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EXTENSIONS
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Edited and extended by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Sep 06 2009
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