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A295934 Number of (not necessarily maximum) 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

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.

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

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Last modified December 2 15:42 EST 2022. Contains 358510 sequences. (Running on oeis4.)