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A295934 Number of (not necessarily maximal) cliques in the n-odd graph. 0

%I

%S 2,8,26,106,442,1849,7723,32176,133706,554269,2292655,9464547,

%T 39002251,160466401,659249461,2704861756,11084629546,45375676501,

%U 185562634951,758155908511,3094982778031,12624593782321,51458942047501,209609423940151,853271593454827

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

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Clique.html">Clique</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/OddGraph.html">Odd Graph</a>

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

%F 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.

%F 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

%t 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}]

%t Table[Piecewise[{{2, n == 1}, {8, n == 2}}, Binomial[2 n - 1, n] + n Binomial[2 n, n]/4 + 1], {n, 20}]

%t 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]

%K nonn,easy,changed

%O 1,1

%A _Eric W. Weisstein_, Nov 29 2017

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Last modified January 27 19:55 EST 2023. Contains 359847 sequences. (Running on oeis4.)