A394266 Number of induced cubes in the n-odd graph.

1, 6, 25, 105, 441, 1848, 7722, 32175, 133705, 554268, 2292654, 9464546, 39002250, 160466400, 659249460, 2704861755, 11084629545, 45375676500, 185562634950, 758155908510, 3094982778030, 12624593782320, 51458942047500, 209609423940150, 853271593454826

Offset

1,2

Links

Table of n, a(n) for n=1..25.

Eric Weisstein's World of Mathematics, Cube Polynomial.

Eric Weisstein's World of Mathematics, Odd Graph.

Formula

G.f.: ((1-3*x)/(1-4*x)^(3/2)-1-x)/2.

For n > 1, a(n) = A092443(n)/2.

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

Mathematica

Table[Binomial[2 n - 1, n - 1] (n + 2 - n KroneckerDelta[1, n])/2, {n, 20}]

Crossrefs

Cf. A092443.

Sequence in context: A267536 A029871 A188178 * A147543 A212258 A048875

Adjacent sequences: A394263 A394264 A394265 * A394267 A394268 A394269

Keyword

nonn,easy

Author

Eric W. Weisstein, Mar 14 2026

Status

approved