A377639 Number of edge cuts in the n-barbell graph.

1, 7, 112, 6748, 1567168, 1434380032, 5313181564672, 80838493938673408, 5049534755835943518208, 1285872353198490183576174592, 1325820676430550921213458275827712, 5508138956812250711370615442510783971328, 91922764576982599075727039533520680008845099008

Offset

1,2

Links

Andrew Howroyd, Table of n, a(n) for n = 1..50

Eric Weisstein's World of Mathematics, Barbell Graph.

Eric Weisstein's World of Mathematics, Edge Cut.

Formula

a(n) = 2*A006125(n)^2 - A001187(n)^2. - Andrew Howroyd, Nov 27 2024

Mathematica

With[{nterms = 20}, Table[2^(k^2 - k + 1), {k, nterms}] - (Rest[CoefficientList[Series[1 + Log[Sum[2^Binomial[k, 2] x^k/k!, {k, 0, nterms}]], {x, 0, nterms}], x]] Range[nterms]!)^2]

Prog

(PARI) seq(n)=my(v=Vec(serlaplace(log(sum(k=0, n, 2^binomial(k, 2)*x^k/k!, O(x*x^n)))))); vector(#v, i, 2^(i*(i-1)+1) - v[i]^2) \\ Andrew Howroyd, Nov 27 2024

Crossrefs

Cf. A001187, A006125.

Sequence in context: A371330 A359927 A010795 * A293456 A099153 A270121

Adjacent sequences: A377636 A377637 A377638 * A377640 A377641 A377642

Keyword

nonn

Author

Eric W. Weisstein, Nov 03 2024

Extensions

a(1)-a(2) prepended and a(6) onwards from Andrew Howroyd, Nov 27 2024

Status

approved