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Stella Octangula Number

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A figurate number of the form

StOct_n=O_n+8Te_(n-1)
(1)
=n(2n^2-1),
(2)

where O_n is an octahedral number and Te_n is a tetrahedral number. The first few are 1, 14, 51, 124, 245, ... (OEIS A007588). The generating function for the stella octangula numbers is

(x(x^2+10x+1))/((x-1)^4)=x+14x^2+51x^3+124x^4+....
(3)

The only known square stella octangula numbers are 1 and 9653449, which correspond to m^2=StOct_n with (m,n)=(1,1) and (m,n)=(3107,169).

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