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 1-3 of 3 results.

A075931 List of codewords in binary lexicode with Hamming distance 5 written as decimal numbers.

Original entry on oeis.org

0, 31, 227, 252, 805, 826, 966, 985, 1354, 1365, 1449, 1462, 1647, 1648, 1676, 1683, 6182, 6201, 6341, 6362, 6915, 6940, 7136, 7167, 7532, 7539, 7567, 7568, 7753, 7766, 7850, 7861, 10315, 10324, 10408, 10423, 11118, 11121, 11149, 11154
Offset: 0

Views

Author

Bob Jenkins (bob_jenkins(AT)burtleburtle.net)

Keywords

Links

Crossrefs

Cf. A075928, A075929, A075930, A075932, A075933, A075924, A075926, A075937.

Programs

  • PARI
    a=vector(40); n=0; for (k=0, 11154, if (n==0 || vecmin(apply(o -> hammingweight(bitxor(k, o)), a[1..n]))>=5, print1 (a[n++]=k", "))) \\ Rémy Sigrist, Feb 09 2021

A075925 Sixth column of triangle A075502.

Original entry on oeis.org

1, 147, 13034, 907578, 54807627, 3016638009, 155726334148, 7676501248416, 365698066506773, 16976491006185711, 772549060467762942, 34614587429584922214, 1532054031119984651839, 67151990527665760714053
Offset: 0

Views

Author

Wolfdieter Lang, Oct 02 2002

Keywords

Comments

The e.g.f. given below is Sum_{m=0..5} A075513(6,m)*exp(7*(m+1)*x)/5!.

Crossrefs

Cf. A075924, A076002.

Programs

  • Mathematica
    CoefficientList[Series[1/Product[1-7k x,{k,6}],{x,0,20}],x] (* Harvey P. Dale, May 25 2012 *)

Formula

a(n) = A075502(n+6, 6) = (7^n)*S2(n+6, 6) with S2(n, m) := A008277(n, m) (Stirling2).
a(n) = Sum_{m=0..5} A075513(6, m)*((m+1)*7)^n/5!.
G.f.: 1/Product_{k=1..6} (1 - 7*k*x).
E.g.f.: (d^6/dx^6)(((exp(7*x)-1)/7)^6)/6! = (-exp(7*x) + 160*exp(14*x) - 2430*exp(21*x) + 10240*exp(28*x) - 15625*exp(35*x) + 7776*exp(42*x))/5!.

A075923 Fourth column of triangle A075502.

Original entry on oeis.org

1, 70, 3185, 120050, 4084101, 130590390, 4012419145, 120031392250, 3525181576301, 102196720335710, 2935410756419505, 83751552660170850, 2377917929557166101, 67273652916778177030, 1898215473677945050265
Offset: 0

Views

Author

Wolfdieter Lang, Oct 02 2002

Keywords

Comments

The e.g.f. given below is Sum_{m=0..3} A075513(4,m)*exp(7*(m+1)*x)/3!.

Crossrefs

Cf. A075922, A075924.

Formula

a(n) = A075502(n+4, 4) = (7^n)*S2(n+4, 4) with S2(n, m) := A008277(n, m) (Stirling2).
a(n) = (-7^n + 24*14^n - 81*21^n + 64*28^n)/3!.
G.f.: 1/Product_{k=1..4} (1 - 7*k*x).
E.g.f.: (d^4/dx^4)(((exp(7*x)-1)/7)^4)/4! = (-exp(7*x) + 24*exp(14*x) - 81*exp(21*x) + 64*exp(28*x))/3!.
Showing 1-3 of 3 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.