cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A001636 A Fielder sequence: a(n) = a(n-1) + a(n-2) - a(n-7), n >= 8.

Original entry on oeis.org

0, 2, 3, 6, 10, 17, 21, 38, 57, 92, 143, 225, 351, 555, 868, 1366, 2142, 3365, 5282, 8296, 13023, 20451, 32108, 50417, 79160, 124295, 195159, 306431, 481139, 755462, 1186184, 1862486, 2924375, 4591702, 7209646, 11320209, 17774393, 27908418, 43820325
Offset: 1

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Keywords

References

  • N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
  • N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Crossrefs

Cf. A013983.

Programs

  • Magma
    I:=[0, 2, 3, 6, 10, 17, 21]; [n le 7 select I[n] else Self(n-1) + Self(n-2) - Self(n-7): n in [1..30]]; // G. C. Greubel, Jan 09 2018
  • Maple
    A001636:=-z*(2+3*z+4*z**2+5*z**3+6*z**4)/(z+1)/(z**5+z**3+z-1); # Simon Plouffe in his 1992 dissertation
    a:= n -> (Matrix([[6,-1$4,4,5]]). Matrix(7, (i,j)-> if (i=j-1) then 1 elif j=1 then [1$2,0$4,-1][i] else 0 fi)^n)[1,1]: seq(a(n), n=1..38); # Alois P. Heinz, Aug 01 2008
  • Mathematica
    LinearRecurrence[{1, 1, 0, 0, 0, 0, -1}, {0, 2, 3, 6, 10, 17, 21}, 50] (* T. D. Noe, Aug 09 2012 *)
  • PARI
    a(n)=if(n<0,0,polcoeff(x^2*(2+x+x^2+x^3+x^4-6*x^5)/(1-x-x^2+x^7)+x*O(x^n),n))
    

Formula

G.f.: x^2*(2+x+x^2+x^3+x^4-6*x^5)/(1-x-x^2+x^7).
a(n) = a(n-2) + a(n-3) + a(n-4) + a(n-5) + a(n-6), n >= 7.

Extensions

Edited by Michael Somos, Feb 17 2002

A023437 Dying rabbits: a(n) = a(n-1) + a(n-2) - a(n-7).

Original entry on oeis.org

0, 1, 1, 2, 3, 5, 8, 13, 20, 32, 50, 79, 124, 195, 306, 481, 755, 1186, 1862, 2924, 4591, 7209, 11319, 17773, 27906, 43817, 68799, 108025, 169615, 266321, 418163, 656578, 1030924, 1618703, 2541602, 3990690
Offset: 0

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Author

Keywords

Crossrefs

See A000045 for the Fibonacci numbers.
First differences are in A013983.

Programs

  • Mathematica
    LinearRecurrence[{1,1,0,0,0,0,-1},{0,1,1,2,3,5,8},40] (* Harvey P. Dale, Nov 06 2013 *)

Formula

G.f.: x/((x-1)*(1+x)*(x^5+x^3+x-1)). [R. J. Mathar, Jul 27 2009]
Showing 1-2 of 2 results.