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International Journal of Mathematics and Mathematical Sciences
Volume 11, Issue 3, Pages 619-623
http://dx.doi.org/10.1155/S0161171288000754

Some further results on Legendre numbers

Department of Mathematics, Last Carolina University, Greenville 27858, North Carolina, USA

Received 12 February 1987

Copyright © 1988 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The Legendre numbers, Pnm, are expressed in terms of those numbers, Pkm1, in the previous column down to Pnm and in terms of those, Pkm, above but in the same column. Other results are given for numbers close to a given number. The limit of the quotient of two consecutive non-zero numbers in any one column is shown to be 1. Bounds for the Legendre numbers are described by circles centered at the origin. A connection between Legendre numbers and Pascal numbers is exhibited by expressing the Legendre numbers in terms of combinations.