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.

A060115 First quotients of A060113.

Original entry on oeis.org

1, 1, 3, 4, 4, 29, 154025, 17807559, 1241018675, 230281392199119, 2, 232684218540127789029851, 154701766297914606806156262617, 1047988403481165390253873, 41235951009889542322570674108482656213249, 25296967137554875194267530420787423406141
Offset: 0

Views

Author

Antti Karttunen, Mar 01 2001

Keywords

Comments

The first few terms factored: 1, 1, 3, 2^2, 2^2, 29, 5*61*101, 3*7*11*127*607.

Links

Programs

Extensions

a(8)-a(15) from Sean A. Irvine, Oct 25 2022

A057542 Maximum cycle length in each permutation between A038776(1) and A038776(A000108(n)).

Original entry on oeis.org

1, 1, 1, 3, 4, 16, 87, 202, 607, 1441, 4708, 41888, 44741, 339108, 1617551
Offset: 0

Views

Author

Antti Karttunen, Sep 07 2000

Keywords

Links

Crossrefs

Cycle lengths of permutation A038776 given in A038774.
Cf. A057543, A057544, A057545.
LCM's of all cycles: A060113.

Programs

  • Maple
    map(lmax,Bf2DfBinTreePermutationCycleLengths(some_value)); (e.g. 10)
bf2df := s -> (btbf2df(binrev(s),0,1)/2); # btbf2df and binrev given in A038776
Bf2DfBinTreePermutationCycleLengths := proc(upto_n) local u,n,a,r,b; a := []; for n from 0 to upto_n do b := []; u := (binomial(2*n,n)/(n+1)); for r from 0 to u-1 do b := [op(b),1+CatalanRank(n,bf2df(CatalanUnrank(n,r)))]; od; a := [op(a),CycleLengths1(b)]; od; RETURN(a); end;
CycleLengths1 := b -> [[(nops(b)-convert(map(nops,convert(b,'disjcyc')),`+`)),`*`,1],op(map(nops,convert(b,'disjcyc')))];
last_term := proc(l) local n: n := nops(l); if(0 = n) then ([]) else (op(n,l)): fi: end:
lmax := proc(a) local e,z; z := 0; for e in a do if whattype(e) = list then e := last_term(e); fi; if e > z then z := e; fi; od; RETURN(z); end;

Extensions

a(11)-a(14) from Sean A. Irvine, Jun 13 2022

A078491 a(n) = lcm(1..Catalan(n)).

Original entry on oeis.org

1, 1, 2, 60, 360360, 219060189739591200, 1749342047920660916901891145781670987072592322134428432000
Offset: 0

Views

Author

Antti Karttunen, Jan 04 2003

Keywords

Comments

For every cycle count LCM-sequence Axxxxxx in A073204 it holds that Axxxxxx(n) divides a(n). And this also applies to similar LCM-sequences induced by other "Catalan bijections", cf. A060113.
The next term (a(7)) has 184 digits. - Harvey P. Dale, Nov 21 2023

Links

Crossrefs

Composition of the sequences A000108 and A003418.

Programs

  • GAP
    List([0..7],n->Lcm([1..Binomial(2*n,n)/(n+1)])); # Muniru A Asiru, Mar 21 2018
  • Mathematica
    Table[LCM@@Range[CatalanNumber[n]],{n,0,7}] (* Harvey P. Dale, Nov 21 2023 *)
  • PARI
    a(n) = lcm([1..binomial(2*n,n)/(n+1)]); \\ Michel Marcus, Mar 21 2018

Formula

a(n) = A003418(A000108(n)).

A038766 Triangle giving number of unbranched catapolytetragons, read by rows.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 3, 3, 2, 1, 3, 9, 7, 4, 1, 5, 16, 29, 23, 10, 1, 5, 27, 62, 99, 69, 25, 1, 7, 39, 132, 275, 351, 229, 70, 1, 7, 55, 221, 643, 1121, 1249, 731, 196, 1, 9, 72, 367, 1278, 2997, 4584, 4437, 2385, 574, 1, 9, 93, 540, 2322, 6678, 13458, 18012, 15597, 7657, 1681
Offset: 0

Views

Author

N. J. A. Sloane, May 03 2000

Keywords

Examples

			1; 1,1; 1,1,1; 1,3,3,2; 1,3,9,7,4; ...

References

  • S. J. Cyvin et al., Unbranched catacondensed polygonal systems containing hexagons and tetragons, Croatica Chem. Acta, 69 (1996), 757-774.

Crossrefs

Last diagonal is A001998.
LCM's of all cycles: A060113.
Showing 1-4 of 4 results.

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

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