A193564 In A014675, replace the n-th occurrence of 1 with n-1 and also replace the n-th occurrence of 2 with n-1.

0, 0, 1, 2, 1, 3, 2, 4, 5, 3, 6, 7, 4, 8, 5, 9, 10, 6, 11, 7, 12, 13, 8, 14, 15, 9, 16, 10, 17, 18, 11, 19, 20, 12, 21, 13, 22, 23, 14, 24, 15, 25, 26, 16, 27, 28, 17, 29, 18, 30, 31, 19, 32, 20, 33, 34, 21, 35, 36, 22, 37, 23, 38, 39, 24, 40, 41, 25, 42

Offset: 1

Author

N. J. A. Sloane, Aug 04 2011

Keywords

• nonn

Comments

An infinite sequence of Langford pairs.

References

• D. E. Knuth, The Art of Computer Programming, Vol. 4A, Section 7, p. 36.

Links

• Paolo Xausa, Table of n, a(n) for n = 1..10946

Crossrefs

Cf. A014552, A014675.

Programs

Maple

A000201 := proc(n) option remember; floor(n*(1+sqrt(5))/2) ; end proc:
A014675 := proc(n) A000201(n+2)-A000201(n+1) ; end proc:
A193564aux := proc(n,piv) local oc,j ; oc := 0 ; for j from 0 to n do if A014675(j) = piv then oc := oc+1 ; end if; end do: oc ; end proc:
A193564 := proc(n) local piv,oc ; piv := A014675(n-1) ; oc := A193564aux(n-1,piv) ; oc-1 ; end proc:
seq(A193564(n),n=1..80) ; # R. J. Mathar, Aug 18 2011

Mathematica

Module[{a = 0, b = 0}, ReplaceAll[SubstitutionSystem[{1 -> {2}, 2 -> {2, 1}}, {1}, {10}][[1]], {1 :> a++, 2 :> b++}]] (* Paolo Xausa, Aug 01 2024 *)