cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

A258487 Number of tangled chains of length k=4.

Original entry on oeis.org

1, 1, 14, 2140, 1017219, 1110178602, 2320017306125, 8278981347401059, 46556715158334549170, 388779284837787599307987, 4605471565794120802036550000, 74633554055057890778698344509705, 1606481673354648219373898238155693682, 44821655543075499856527523557216582931002
Offset: 1

Views

Author

Sara Billey, Matjaz Konvalinka, and Frederick A. Matsen IV, May 31 2015

Keywords

Comments

Tangled chains are ordered lists of k rooted binary trees with n leaves and a matching between each leaf from the i-th tree with a unique leaf from the (i+1)-st tree up to isomorphism on the binary trees. This sequence fixes k=4, and n = 1,2,3,...

References

  • R. Page, Tangled trees: phylogeny, cospeciation, and coevolution, The University of Chicago Press, 2002.

Links

Crossrefs

Cf. A000123 (binary partitions), A258620 (tanglegrams), A258485, A258486, A258487, A258488, A258489 (tangled chains), A259114 (unordered tanglegrams).

Formula

t(n) = Sum_{b=(b(1),...,b(t))} Product_{i=2..t} (2(b(i)+...+b(t))-1)^4)/z(b) where the sum is over all binary partitions of n and z(b) is the size of the stabilizer of a permutation of cycle type b under conjugation.

A258488 Number of tangled chains of length k=5.

Original entry on oeis.org

1, 1, 41, 31732, 106420469, 1046976648840, 24085106680575625, 1117767454807330938472, 94308987414050519542935029, 13390317159105772877158700776107, 3014130596940522685213135526859317500, 1025828273466214412416440210115479183065903, 507888918625036626314714587415852381698509422634
Offset: 1

Views

Author

Sara Billey, Matjaz Konvalinka, and Frederick A. Matsen IV, May 31 2015

Keywords

Comments

Tangled chains are ordered lists of k rooted binary trees with n leaves and a matching between each leaf from the i-th tree with a unique leaf from the (i+1)-st tree up to isomorphism on the binary trees. This sequence fixes k=5, and n = 1,2,3,...

References

  • R. Page, Tangled trees: phylogeny, cospeciation, and coevolution, The University of Chicago Press, 2002.

Links

Crossrefs

Cf. A000123 (binary partitions), A258620 (tanglegrams), A258485, A258486, A258487, A258488, A258489 (tangled chains), A259114 (unordered tanglegrams).

Formula

t(n) = Sum_{b=(b(1),...,b(t))} Product_{i=2..t} (2(b(i)+...+b(t))-1)^5)/z(b) where the sum is over all binary partitions of n and z(b) is the size of the stabilizer of a permutation of cycle type b under conjugation.

A258489 Number of tangled chains of length k=6.

Original entry on oeis.org

1, 1, 122, 474883, 11168414844, 989169269347359, 250335000079534559375, 151038989624520433840089358, 191158216491241179675824199407135, 461408865973380293005829125668717407727, 1973397409908124305318632313047269426852165625, 14104214451439837037643144221899175649593123932192274
Offset: 1

Views

Author

Sara Billey, Matjaz Konvalinka, and Frederick A. Matsen IV, May 31 2015

Keywords

Comments

Tangled chains are ordered lists of k rooted binary trees with n leaves and a matching between each leaf from the i-th tree with a unique leaf from the (i+1)-st tree up to isomorphism on the binary trees. This sequence fixes k=6, and n = 1,2,3,...

References

  • R. Page, Tangled trees: phylogeny, cospeciation, and coevolution, The University of Chicago Press, 2002.

Links

Crossrefs

Cf. A000123 (binary partitions), A258620 (tanglegrams), A258485, A258486, A258487, A258488, A258489 (tangled chains), A259114 (unordered tanglegrams).

Formula

t(n) = Sum_{b=(b(1),...,b(t))} Product_{i=2..t} (2(b(i)+...+b(t))-1)^6)/z(b) where the sum is over all binary partitions of n and z(b) is the size of the stabilizer of a permutation of cycle type b under conjugation.

A258486 Number of tangled chains of length k=3.

Original entry on oeis.org

1, 1, 5, 151, 9944, 1196991, 226435150, 61992679960, 23198439767669, 11380100883484302, 7087878538028540725, 5465174495550911165171, 5111311778783673593594175, 5701234859347275019419890715, 7477492710871626347942014991975, 11393306956061559325223329489826611, 19958666934810234750929365717573438949, 39835206091758734935374720734513530255512, 89867076346063005007676287874769844881101800, 227547795689116560408812799327387232156371842150
Offset: 1

Views

Author

Sara Billey, May 31 2015

Keywords

Comments

Tangled chains are ordered lists of k rooted binary trees with n leaves and a matching between each leaf from the i-th tree with a unique leaf from the (i+1)st tree up to isomorphism on the binary trees. This sequence fixes k=3, and n = 1,2,3,...

References

  • R. Page, Tangled trees: phylogeny, cospeciation, and coevolution, The University of Chicago Press, 2002.

Links

Crossrefs

Cf. A000123 (binary partitions), A258485 (tanglegrams), A258487, A258488, A258489.

Formula

t(n) = Sum_{b=(b(1),...,b(t))} Product_{i=2..t} (2(b(i)+...+b(t))-1)^3)/z(b) where the sum is over all binary partitions of n and z(b) is the size of the stabilizer of a permutation of cycle type b under conjugation.
Showing 1-4 of 4 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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