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Gnomonic Number

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GnomonicNumber

A figurate number of the form g_n=2n-1 giving the area of the square gnomon obtained by removing a square of side n-1 from a square of side n,

g_n=n^2-(n-1)^2
(1)
=2n-1.
(2)

The gnomonic numbers are therefore equivalent to the odd numbers, and the first few are 1, 3, 5, 7, 9, 11, ... (OEIS A005408). The generating function for the gnomonic numbers is

(x(1+x))/((x-1)^2)=x+3x^2+5x^3+7x^4+....
(3)

See also

Figurate Number, Gnomon, Odd Number, Odd Number Theorem

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References

Merzbach, U. C. and Boyer, C. B. A History of Mathematics, 3rd ed. New York: Wiley, p. 49, 1991.Sloane, N. J. A. Sequence A005408/M2400 in "The On-Line Encyclopedia of Integer Sequences."

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Gnomonic Number

Cite this as:

Weisstein, Eric W. "Gnomonic Number." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/GnomonicNumber.html

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