A072373 Complexity of doubled cycle (regarding case n = 2 as a graph).

1, 4, 75, 384, 1805, 8100, 35287, 150528, 632025, 2620860, 10759331, 43804800, 177105253, 711809364, 2846259375, 11330543616, 44929049777, 177540878700, 699402223099, 2747583822720, 10766828545725, 42095796462852, 164244726238343

Offset

1,2

References

G. Kreweras, Complexite et circuits Euleriens dans les sommes tensorielles de graphes, J. Combin. Theory, B 24 (1978), 202-212.

Links

Table of n, a(n) for n=1..23.

Formula

G.f.: -8x^2+x(1+2x-10x^2+2x^3+x^4)/((1-x)*(1-4x+x^2))^2.

a(n)=10a(n-1)-35a(n-2)+52a(n-3)-35a(n-4)+10a(n-5)-a(n-6), n>8.

Prog

(PARI) /* prism (or doubled cycle) graph with n vertices */ prism(n)=if(n%2, [; ], matrix(n, n, i, j, i!=j && ((abs(i-j)==1 && (i+j)!=n+1) || (abs(i-j)==n/2-1 && (i+j)%n==n/2+1) || abs(i-j)==n/2)))
(PARI) /* treenumber (or complexity) of a graph */ treenumber(m)=local(n); n=matdim(m); if(n, matdet(adj2laplace(m)+matone(n))/n^2)
(PARI) /* convert adjacency matrix to laplacian matrix */ adj2laplace(m)=local(l, n); n=matdim(m); matdiagonal(m*vectorv(n, i, 1))-m
(PARI) /* matrix J of all ones */ matone(n)=matrix(n, n, i, j, 1) /* dimension of a square matrix */ matdim(m)=matsize(m)[1]
(PARI) a(n)=treenumber(prism(2*n))
(PARI) a(n)=if(n<0, 0, polcoeff(-8*x^2+x*(1+2*x-10*x^2+2*x^3+x^4)/((1-x)*(1-4*x+x^2))^2+x*O(x^n), n))

Crossrefs

Apart from a(2) coincides with A006235.

Sequence in context: A046057 A280889 A257367 * A006412 A206456 A137220

Adjacent sequences: A072370 A072371 A072372 * A072374 A072375 A072376

Keyword

nonn,easy

Author

Michael Somos, Jul 19 2002

Status

approved