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.

A144872 Periods of the rows of A144871.

Original entry on oeis.org

1, 1, 3, 8, 5, 72, 7, 32, 27, 400, 11, 864, 13, 784, 675, 128, 17, 2592, 19, 1600, 1323, 3872, 23, 3456, 125, 5408, 243, 3136, 29, 324000, 31, 512, 9801, 18496, 6125, 31104, 37, 23104, 13689, 32000, 41, 254016, 43, 15488, 30375, 33856, 47
Offset: 1

Views

Author

Alois P. Heinz, Sep 23 2008

Keywords

Crossrefs

Cf. A144871, A007318, A133900.

A144865 Shadow transform of C(n+3,4) = A000332(n+3).

Original entry on oeis.org

1, 1, 1, 1, 4, 1, 4, 1, 2, 4, 4, 1, 4, 5, 6, 1, 4, 3, 4, 4, 5, 3, 4, 1, 4, 4, 2, 3, 4, 5, 4, 1, 5, 6, 16, 2, 4, 3, 6, 4, 4, 5, 4, 4, 9, 5, 4, 1, 4, 6, 7, 2, 4, 2, 16, 2, 7, 4, 4, 5, 4, 5, 11, 1, 16, 7, 4, 7, 6, 16, 4, 2, 4, 4, 5, 2, 16, 5, 4, 4, 2, 6, 4, 5, 16, 3, 5, 6, 4, 13, 16, 3, 6, 5, 16, 1, 4, 6, 10, 3, 4
Offset: 1

Views

Author

Alois P. Heinz, Sep 23 2008

Keywords

Links

  • Alois P. Heinz, Table of n, a(n) for n = 1..1000
  • Lorenz Halbeisen and Norbert Hungerbuehler, Number theoretic aspects of a combinatorial function, Notes on Number Theory and Discrete Mathematics 5(4) (1999), 138-150. (ps, pdf); see Definition 7 for the shadow transform.
  • N. J. A. Sloane, Transforms.

Crossrefs

4th column of A144871. Cf. A007318.

Programs

  • Maple
    shadow:= proc(p) proc(n) local j; add (`if` (modp(p(j), n)=0, 1,0), j=0..n-1) end end: f:= proc(k) proc(n) binomial (n+k-1,k) end end: a:= n-> shadow (f(4))(n): seq (a(n), n=1..120);

A144866 Shadow transform of C(n+4,5) = A000389(n+4).

Original entry on oeis.org

1, 1, 2, 1, 1, 3, 5, 2, 4, 1, 5, 3, 5, 8, 1, 2, 5, 6, 5, 1, 11, 7, 5, 6, 1, 7, 4, 8, 5, 4, 5, 2, 11, 8, 4, 7, 5, 7, 11, 2, 5, 15, 5, 9, 4, 8, 5, 6, 5, 1, 12, 8, 5, 6, 3, 13, 12, 7, 5, 4, 5, 8, 22, 2, 8, 16, 5, 11, 11, 6, 5, 12, 5, 7, 1, 8, 25, 16, 5, 2, 4, 8, 5, 22, 5, 7, 11, 15, 5, 6, 25, 8, 11, 8, 5, 5
Offset: 1

Views

Author

Alois P. Heinz, Sep 23 2008

Keywords

Links

  • Alois P. Heinz, Table of n, a(n) for n = 1..10000
  • Lorenz Halbeisen and Norbert Hungerbuehler, Number theoretic aspects of a combinatorial function, Notes on Number Theory and Discrete Mathematics 5(4) (1999), 138-150. (ps, pdf); see Definition 7 for the shadow transform.
  • N. J. A. Sloane, Transforms.

Crossrefs

5th column of A144871. Cf. A007318.

Programs

  • Maple
    shadow:= proc(p) proc(n) local j;
           add(`if`(modp(p(j), n)=0, 1, 0), j=0..n-1) end
         end:
f:= proc(k) proc(n) binomial (n+k-1,k) end end:
a:= n-> shadow(f(5))(n):
seq(a(n), n=1..120);

A144867 Shadow transform of C(n+5,6) = A000579(n+5).

Original entry on oeis.org

1, 1, 1, 2, 1, 3, 6, 1, 1, 2, 6, 4, 6, 9, 2, 1, 6, 1, 6, 2, 11, 8, 6, 3, 2, 9, 1, 14, 6, 6, 6, 1, 10, 10, 9, 4, 6, 8, 12, 3, 6, 15, 6, 14, 5, 9, 6, 4, 6, 3, 12, 13, 6, 1, 8, 12, 13, 9, 6, 7, 6, 9, 11, 1, 13, 17, 6, 17, 11, 15, 6, 2, 6, 9, 5, 13, 36, 16, 6, 2, 1, 10, 6, 29, 10, 8, 10, 15, 6, 5, 36, 14
Offset: 1

Views

Author

Alois P. Heinz, Sep 23 2008

Keywords

Links

Crossrefs

6th column of A144871.
Cf. A007318.

Programs

  • Maple
    shadow:= proc(p) proc(n) add(`if`(modp(p(j), n)=0, 1, 0), j=0..n-1) end end:
f:= proc(k) proc(n) binomial(n+k-1, k) end end:
a:= shadow(f(6)):
seq(a(n), n=1..100);

A144868 Shadow transform of C(n+6,7) = A000580(n+6).

Original entry on oeis.org

1, 1, 1, 3, 2, 4, 1, 4, 3, 3, 7, 6, 7, 1, 5, 4, 7, 5, 7, 6, 1, 12, 7, 10, 4, 12, 3, 1, 7, 9, 7, 4, 15, 12, 1, 12, 7, 12, 16, 11, 7, 1, 7, 22, 10, 12, 7, 11, 1, 6, 16, 22, 7, 6, 16, 6, 16, 12, 7, 18, 7, 12, 4, 4, 20, 27, 7, 24, 16, 6, 7, 19, 7, 12, 9, 22, 4, 27, 7, 11, 3, 12, 7, 5, 17, 12, 15, 36, 7
Offset: 1

Views

Author

Alois P. Heinz, Sep 23 2008

Keywords

Links

Crossrefs

7th column of A144871.
Cf. A007318.

Programs

  • Maple
    a:= n-> add(`if`(modp(binomial(j+6, 7), n)=0, 1, 0), j=0..n-1):
seq(a(n), n=1..120);

A144869 Shadow transform of C(n+7,8) = A000581(n+7).

Original entry on oeis.org

1, 1, 2, 1, 3, 1, 1, 1, 6, 2, 8, 1, 8, 1, 8, 1, 8, 6, 8, 1, 3, 6, 8, 1, 6, 7, 6, 1, 8, 7, 8, 1, 21, 14, 4, 7, 8, 8, 21, 1, 8, 2, 8, 8, 21, 7, 8, 1, 2, 6, 21, 4, 8, 5, 26, 1, 21, 7, 8, 6, 8, 13, 11, 1, 28, 21, 8, 11, 21, 10, 8, 6, 8, 5, 16, 4, 11, 21, 8, 1, 6, 8, 8, 2, 26, 6, 21, 7, 8, 20, 12, 7, 21, 13
Offset: 1

Views

Author

Alois P. Heinz, Sep 23 2008

Keywords

Links

Crossrefs

8th column of A144871. Cf. A007318.

Programs

  • Maple
    shadow:= proc(p) proc(n) local j; add (`if` (modp(p(j), n)=0, 1,0), j=0..n-1) end end: f:= proc(k) proc(n) binomial (n+k-1,k) end end: a:= n-> shadow (f(8))(n): seq (a(n), n=1..100);

A144870 Shadow transform of C(n+8,9) = A000582(n+8).

Original entry on oeis.org

1, 1, 1, 1, 4, 1, 2, 1, 1, 5, 9, 1, 9, 3, 1, 2, 9, 1, 9, 6, 2, 12, 9, 1, 8, 13, 1, 4, 9, 6, 9, 2, 8, 16, 9, 1, 9, 13, 9, 7, 9, 3, 9, 18, 1, 13, 9, 2, 4, 12, 8, 14, 9, 1, 37, 4, 8, 13, 9, 8, 9, 16, 1, 2, 38, 11, 9, 20, 7, 16, 9, 1, 9, 12, 13, 14, 21, 16, 9, 12, 1, 13, 9, 6, 37, 12, 16, 20, 9, 8, 22, 17
Offset: 1

Views

Author

Alois P. Heinz, Sep 23 2008

Keywords

Links

Crossrefs

9th column of A144871. Cf. A007318.

Programs

  • Maple
    shadow:= proc(p) proc(n) local j; add (`if` (modp(p(j), n)=0, 1,0), j=0..n-1) end end: f:= proc(k) proc(n) binomial (n+k-1,k) end end: a:= n-> shadow (f(9))(n): seq (a(n), n=1..100);
Showing 1-7 of 7 results.

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