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A183556 Positions of the records of the negative integers in A179319; a(n) is the first position in A179319 equal to -n. 4
1, 3, 37, 71, 681, 1291, 12237, 23183, 219601, 416019, 3940597, 7465175 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The g.f. of A059973 is (x+x^2-2*x^3)/(1-4*x^2-x^4).

LINKS

Table of n, a(n) for n=1..12.

FORMULA

Conjecture: the positions of the records of the negative integers in A179319 are given by:

* a(2n-1) = A059973(4n-1) - 1 for n>=1;

* a(2n) = A059973(4n) - 1 for n>=1.

EXAMPLE

Define WL(x) and WU(x) to be respectively the characteristic functions of the lower (A000201) and upper (A001950) Wythoff sequences:

* WL(x) = 1 + x + x^3 + x^4 + x^6 + x^8 + x^9 + x^11 +...+ x^[n*phi] +...

* WU(x) = 1 + x^2 + x^5 + x^7 + x^10 + x^13 + x^15 +...+ x^[n*(phi+1)] +...

then the g.f. of A179319 is the product:

* WL(-x)*WU(x) = 1 - x + x^2 - 2*x^3 + x^4 + x^6 + x^7 + x^10 - x^11 + x^12 + x^13 + x^14 + 2*x^15 +...+ A179319(n)*x^n +...

in which it is conjectured that the following holds:

* A179319(A059973(4n-1)-1) = -(2n-1) for n>=1;

* A179319(A059973(4n)-1) = -(2n) for n>=1.

CROSSREFS

Cf. A183555, A179319, A059973, A183557, A000201, A001950.

Sequence in context: A056408 A056398 A092074 * A107183 A031919 A151730

Adjacent sequences:  A183553 A183554 A183555 * A183557 A183558 A183559

KEYWORD

nonn,more

AUTHOR

Paul D. Hanna, Jan 12 2011

EXTENSIONS

Terms a(10) - a(12) computed by D. S. McNeil, Dec 28 2010.

STATUS

approved

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Last modified May 19 18:35 EDT 2022. Contains 353847 sequences. (Running on oeis4.)