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%I #12 Mar 18 2026 04:35:09
%S 1,6,25,105,441,1848,7722,32175,133705,554268,2292654,9464546,
%T 39002250,160466400,659249460,2704861755,11084629545,45375676500,
%U 185562634950,758155908510,3094982778030,12624593782320,51458942047500,209609423940150,853271593454826
%N Number of induced cubes in the n-odd graph.
%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CubePolynomial.html">Cube Polynomial</a>.
%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/OddGraph.html">Odd Graph</a>.
%F G.f.: ((1-3*x)/(1-4*x)^(3/2)-1-x)/2.
%F For n > 1, a(n) = A092443(n)/2.
%F D-finite with recurrence: (-25*n^2+19*n+12)*a(n) + 18*(2*n-1)*(n-2)*a(n-1) + 4*(n-1)*(n+1)*a(n+1), with initial terms a(1)=1, a(2)=6, a(3)=25. - _Georg Fischer_, Mar 17 2026
%t Table[Binomial[2 n - 1, n - 1] (n + 2 - n KroneckerDelta[1, n])/2, {n, 20}]
%Y Cf. A092443.
%K nonn,easy
%O 1,2
%A _Eric W. Weisstein_, Mar 14 2026