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

1,4

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

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 *)

Crossrefs

Cf. A014552, A014675.

Sequence in context: A214370 A227859 A026272 * A022447 A117194 A340647

Adjacent sequences: A193561 A193562 A193563 * A193565 A193566 A193567

Keyword

nonn

Author

N. J. A. Sloane, Aug 04 2011

Status

approved