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 1-7 of 7 results.

A126298 Fixed points of the permutation A125987/A125988.

Original entry on oeis.org

0, 1, 2, 3, 4, 8, 9, 22, 23, 47, 64, 65, 86, 162, 196, 197, 259, 443, 501, 625, 626, 1205, 1743, 2055, 2056, 2707, 5334, 6917, 6918, 7540, 22372, 23713, 23714, 62571, 64277, 82499, 82500, 109605, 253759, 290511, 290512, 579423, 621466, 653479
Offset: 0

Views

Author

Antti Karttunen, Jan 02 2007

Keywords

Comments

Those i, for which A125987(i)=i, or equivalently A125985(A125985(i))=i. A126299 shows the same fixed points using factorial code as employed in Vaillé's paper.

Links

Crossrefs

Superset of A126300.

A126295 Number of fixed points in range [A014137(n-1)..A014138(n-1)] of permutation A125987/A125988.

Original entry on oeis.org

1, 1, 2, 2, 2, 3, 4, 5, 4, 4, 4, 4, 4, 7, 8, 7, 6, 10
Offset: 0

Views

Author

Antti Karttunen, Jan 02 2007

Keywords

Crossrefs

Fixed points themselves are given in A126298/A126299.

A126294 Number of cycles in range [A014137(n-1)..A014138(n-1)] of permutation A125987/A125988.

Original entry on oeis.org

1, 1, 2, 3, 4, 8, 16, 17, 32, 40, 44, 60, 88, 100
Offset: 0

Views

Author

Antti Karttunen, Jan 02 2007

Keywords

Comments

The number of orbits (equivalence classes) to which the square of Vaille's automorphism partitions the set of A000108(n) Dyck paths of semilength n.

Crossrefs

a(2n) = 2*A126291(2n) for n>0.

A126296 Maximum cycle size in range [A014137(n-1)..A014138(n-1)] of permutation A125987/A125988.

Original entry on oeis.org

1, 1, 1, 3, 6, 13, 30, 125, 223, 719, 4866, 12916, 51495, 153945
Offset: 0

Views

Author

Antti Karttunen, Jan 02 2007

Keywords

Comments

The size of a largest orbit to which the square of Vaille's automorphism partitions the set of A000108(n) Dyck paths of semilength n.

Crossrefs

For n>0, it seems that A126292(2n) = 2*a(2n).

A126297 Least common multiple of all cycle sizes in range [A014137(n-1)..A014138(n-1)] of permutation A125987/A125988.

Original entry on oeis.org

1, 1, 1, 3, 6, 390, 13860, 23892750, 80215013340, 9851050382488595280, 694858921540030774800, 344551675909308833470705200, 1955049249155875335764556836119978483886656454640
Offset: 0

Views

Author

Antti Karttunen, Jan 02 2007

Keywords

Crossrefs

Cf. A126293.

A125988 Signature-permutation of the square of A125986.

Original entry on oeis.org

0, 1, 2, 3, 4, 7, 5, 6, 8, 9, 16, 12, 17, 21, 10, 13, 11, 14, 20, 18, 15, 19, 22, 23, 42, 30, 45, 56, 26, 35, 31, 44, 58, 48, 46, 57, 63, 24, 32, 27, 33, 50, 25, 29, 28, 37, 53, 47, 40, 54, 62, 43, 36, 34, 38, 41, 49, 39, 51, 61, 59, 55, 52, 60, 64, 65, 121, 84, 128, 163, 72
Offset: 0

Views

Author

Antti Karttunen, Jan 02 2007

Keywords

Links

Crossrefs

Inverse: A125987. a(n) = A125986(A125986(n)).

A126718 a(n) is the number of nonnegative integers k less than 10^n such that the decimal representation of k lacks the digits 1,2,3, at least one of digits 4,5, at least one of digits 6,7 and at least one of digits 8,9.

Original entry on oeis.org

7, 43, 235, 1171, 5467, 24403, 105595, 447091, 1864027, 7686163, 31440955, 127865011, 517788187, 2090186323, 8417944315, 33843570931, 135890057947, 545108340883, 2185079263675, 8754257900851, 35058860433307, 140360940805843, 561820285607035
Offset: 1

Views

Author

Aleksandar M. Janjic and Milan Janjic, Feb 13 2007

Keywords

Links

Crossrefs

Cf. A125910, A125945, A125946, A125947, A125948, A125880, A125630, A125987, A125904, A125858, A125909, A125908, A126646, A126645, A126644, A126643, A126642, A126641, A126640, A126639, A126635, A126634, A126633, A126632, A126631, A126628, A126627.

Programs

  • Magma
    [8*4^n-12*3^n+6*2^n-1: n in [1..30]]; // Vincenzo Librandi, May 31 2011
  • Maple
    a:=n->8*4^n-12*3^n+6*2^n-1;
  • Mathematica
    LinearRecurrence[{10,-35,50,-24},{7, 43, 235, 1171},23] (* James C. McMahon, Dec 27 2024 *)
  • PARI
    Vec(-x*(24*x^3-50*x^2+27*x-7) / ((x-1)*(2*x-1)*(3*x-1)*(4*x-1)) + O(x^100)) \\ Colin Barker, Feb 22 2015

Formula

a(n) = 8*4^n - 12*3^n + 6*2^n - 1.
a(n) = 10*a(n-1) - 35*a(n-2) + 50*a(n-3) - 24*a(n-4). - Colin Barker, Feb 22 2015
G.f.: -x*(24*x^3 - 50*x^2 + 27*x - 7) / ((x-1)*(2*x-1)*(3*x-1)*(4*x-1)). - Colin Barker, Feb 22 2015
Showing 1-7 of 7 results.

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

Content is available under The OEIS End-User License Agreement.