A065169 Permutation t->t-2 of Z, folded to N.
5, 3, 7, 1, 9, 2, 11, 4, 13, 6, 15, 8, 17, 10, 19, 12, 21, 14, 23, 16, 25, 18, 27, 20, 29, 22, 31, 24, 33, 26, 35, 28, 37, 30, 39, 32, 41, 34, 43, 36, 45, 38, 47, 40, 49, 42, 51, 44, 53, 46, 55, 48, 57, 50, 59, 52, 61, 54, 63, 56, 65, 58, 67, 60, 69, 62, 71, 64, 73, 66, 75, 68
Offset: 1
Links
- Vincenzo Librandi, Table of n, a(n) for n = 1..1000
- Joe Buhler and R. L. Graham, Juggling Drops and Descents, Amer. Math. Monthly, 101, (no. 6) 1994, 507 - 519.
- Index entries for sequences that are permutations of the natural numbers
- Index entries for linear recurrences with constant coefficients, signature (1,1,-1).
Crossrefs
Inverse permutation to A065165.
Programs
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Mathematica
CoefficientList[Series[(x^6 - x^5 + 4 x^4 - 4 x^3 - x^2 - 2 x + 5)/((x - 1)^2 (x + 1)), {x, 0, 100}], x] (* Vincenzo Librandi, Mar 08 2014 *) -
PARI
Vec(x*(x^6-x^5+4*x^4-4*x^3-x^2-2*x+5)/((x-1)^2*(x+1)) + O(x^100)) \\ Colin Barker, Mar 07 2014
Formula
Let f: Z -> N be given by f(z) = 2z if z>0 else 2|z|+1, with inverse g(z) = z/2 if z even else (1-z)/2. Then a(n) = f(g(n)-2).
G.f.: x*(x^6-x^5+4*x^4-4*x^3-x^2-2*x+5) / ((x-1)^2*(x+1)). - Colin Barker, Feb 18 2013
a(n) = -4*(-1)^n+n for n>4. a(n) = a(n-1)+a(n-2)-a(n-3) for n>7. - Colin Barker, Mar 07 2014
Comments