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 A165157 Zero followed by partial sums of A133622. 5
 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; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS A133622 is a toothed sequence. Interleaving of A055998 and A034856. LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..10000 Index entries for linear recurrences with constant coefficients, signature (1,2,-2,-1,1). FORMULA a(0) = 0, a(2*n) = a(2*n-1) + n + 1, a(2*n+1) = a(2*n) + 1. a(n) = (n^2+10*n)/8 if n is even, a(n) = (n^2+8*n-1)/8 if n is odd. a(2*k) = A055998(k) = k*(k+5)/2; a(2*k+1) = A034856(k+1) = k*(k+5)/2+1. 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. - Klaus Brockhaus, Sep 06 2009 a(n) = (2*n*(n+9)-1+(2*n+1)*(-1)^n)/16. - Klaus Brockhaus, Sep 06 2009 a(n) = n+binomial(1+floor(n/2),2). - Mircea Merca, Feb 18 2012 G.f.: x*(1+2*x-x^2-x^3)/((1-x)^3*(1+x)^2). - Klaus Brockhaus, Sep 06 2009 From Stefano Spezia, Jul 10 2020: (Start) E.g.f.: (x*(9 + x)*cosh(x) + (-1 + 11*x + x^2)*sinh(x))/8. a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4) + a(n-5) for n > 4. (End) EXAMPLE From Stefano Spezia, Jul 10 2020: (Start) Illustration of the initial terms for n > 0: o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o (1) (3) (4) (7) (8) (12) (End) PROG (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] ]; // 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] ]; // Klaus Brockhaus, Sep 06 2009 (Haskell) a165157 n = a165157_list !! n a165157_list = scanl (+) 0 a133622_list -- Reinhard Zumkeller, Feb 20 2015 CROSSREFS 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: A026449 A286904 A282166 * A182079 A129819 A025032 Adjacent sequences: A165154 A165155 A165156 * A165158 A165159 A165160 KEYWORD nonn,easy AUTHOR Jaroslav Krizek, Sep 05 2009 EXTENSIONS Edited and extended by Klaus Brockhaus, Sep 06 2009 STATUS approved

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Last modified May 20 11:55 EDT 2024. Contains 372712 sequences. (Running on oeis4.)