bibkey: sloane2018a160627 authors: N. J. A. Sloane; Robert Israel year: 2018 title: “OEIS A160627, Numerator of Laguerre(n, 4)” doi: null url: https://oeis.org/A160627 claim: “%N Numerator of Laguerre(n, 4). %C Conjecture: all terms are odd. - Robert Israel, Mar 29 2018 %N Denominator of Laguerre(n, 4). %C Conjecture: all terms are odd. - Robert Israel, Mar 29 2018” strata_touched:
- D5/S3/ArithSums/IsraelLaguerreFourParity license: citation-only triage: anchor
OEIS A160627 and A160628
OEIS A160627 records the NAME (%N, verbatim):
Numerator of Laguerre(n, 4).
Its COMMENT conjecture (%C, verbatim) is:
Conjecture: all terms are odd. - Robert Israel, Mar 29 2018
OEIS A160628 records the NAME (%N, verbatim):
Denominator of Laguerre(n, 4).
Its COMMENT conjecture (%C, verbatim) is:
Conjecture: all terms are odd. - Robert Israel, Mar 29 2018
The sequence AUTHOR line is _N. J. A. Sloane_, Nov 14 2009; the year 2018
records the date of Robert Israel’s two conjecture comments. Both conjectures
are proved by the one theorem result, whose two conjuncts establish numerator
and denominator parity. The definition L is the explicit binomial-sum
definition of the classical Laguerre polynomial at x = 4, rather than an
application of a Mathlib Laguerre polynomial API.
The first seven reduced numerator-denominator pairs are (1,1), (-3,1),
(1,1), (7,3), (1,1), (-13,15), and (-83,45), agreeing with the two
OEIS sequences.
Verified locator
- URL: https://oeis.org/A160627
- A160627 NAME (
%N, verbatim): Numerator of Laguerre(n, 4). - A160627 COMMENT (
%C, verbatim): Conjecture: all terms are odd. - Robert Israel, Mar 29 2018 - A160628 NAME (
%N, verbatim): Denominator of Laguerre(n, 4). - A160628 COMMENT (
%C, verbatim): Conjecture: all terms are odd. - Robert Israel, Mar 29 2018 - AUTHOR (
%A, verbatim): N. J. A. Sloane, Nov 14 2009