A295934 Number of (not necessarily maximal) cliques in the n-odd graph.

2, 8, 26, 106, 442, 1849, 7723, 32176, 133706, 554269, 2292655, 9464547, 39002251, 160466401, 659249461, 2704861756, 11084629546, 45375676501, 185562634951, 758155908511, 3094982778031, 12624593782321, 51458942047501, 209609423940151, 853271593454827

Offset

1,1

Links

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

Eric Weisstein's World of Mathematics, Clique

Eric Weisstein's World of Mathematics, Odd Graph

Formula

a(n) = binomial(2*n - 1, n) + n*binomial(2*n, n)/4 + 1 for n > 2.

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

D-finite with recurrence n*a(n) +(-7*n+4)*a(n-1) +6*(2*n-3)*a(n-2) +2*(-3*n+7)=0. - R. J. Mathar, Jan 25 2023

Mathematica

Table[Piecewise[{{2, n == 1}, {8, n == 2}}, Binomial[2 n - 1, n] + (2 n - 1) Binomial[2 n - 3, n - 2] + 1], {n, 20}]
Table[Piecewise[{{2, n == 1}, {8, n == 2}}, Binomial[2 n - 1, n] + n Binomial[2 n, n]/4 + 1], {n, 20}]
CoefficientList[Series[(-1 + Sqrt[1 - 4 x] + x (-1 + 1/(1 - 4 x)^(3/2) + 4/Sqrt[1 - 4 x] - 2/(-1 + x) + 2 x))/(2 x), {x, 0, 20}], x]

Crossrefs

Sequence in context: A348240 A128238 A110156 * A187151 A150674 A150675

Adjacent sequences: A295931 A295932 A295933 * A295935 A295936 A295937

Keyword

nonn,easy

Author

Eric W. Weisstein, Nov 29 2017

Status

approved