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A295934 Number of (not necessarily maximal) cliques in the n-odd graph. 0
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
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
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Nov 29 2017
STATUS
approved

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Last modified April 18 20:26 EDT 2024. Contains 371781 sequences. (Running on oeis4.)