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.

Previous Showing 31-35 of 35 results.

A001886 Hit polynomials.

Original entry on oeis.org

3, 6, 44, 180, 1407, 10384, 92896, 911512, 9913152, 117788056, 1519021046, 21123287848, 315034832581, 5015656588706, 84899016219708, 1522394744470356, 28828385427350245, 574839634258405032, 12039133083940334978, 264216869431056251276, 6063573884814663905952
Offset: 3

Views

Author

N. J. A. Sloane

Keywords

References

  • J. Riordan, The enumeration of permutations with three-ply staircase restrictions, unpublished memorandum, Bell Telephone Laboratories, Murray Hill, NJ, Oct 1963. (See A001883)
  • N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
  • N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Crossrefs

Fourth column of A080018.
Cf. A001883-A001891.

Extensions

More terms from Vladeta Jovovic and Vladimir Baltic, Jan 20 2003
a(21)-a(23) from Vaclav Kotesovec, Oct 10 2017

A001888 Hit polynomials.

Original entry on oeis.org

1, 1, 1, 4, 21, 122, 849, 6719, 59873, 593686, 6483027, 77309508, 999569969, 13927664613, 208044077633, 3316415176712, 56193522437465, 1008499234742158, 19110533105114433, 381290148293261075, 7989548583615385153, 175418232627066361514, 4027213499971769192903, 96489861550805864197512
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

References

  • J. Riordan, The enumeration of permutations with three-ply staircase restrictions, unpublished memorandum, Bell Telephone Laboratories, Murray Hill, NJ, Oct 1963. (See A001883)
  • N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
  • N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Crossrefs

Second column of A080061.
Cf. A001883-A001891.

Extensions

More terms from Vladeta Jovovic, Vladimir Baltic, Jan 23 2003
a(21)-a(24) from Vaclav Kotesovec, Oct 10 2017

A001889 Hit polynomials.

Original entry on oeis.org

1, 4, 8, 38, 209, 1400, 10849, 95516, 938441, 10179149, 120748974, 1554688240, 21588485677, 321561688748, 5113709884902, 86469576394028, 1549114961438599, 29309613834899864, 583986501706555597, 12222118836543561940, 268060239251978779839, 6148136982942476816891
Offset: 2

Views

Author

N. J. A. Sloane

Keywords

References

  • J. Riordan, The enumeration of permutations with three-ply staircase restrictions, unpublished memorandum, Bell Telephone Laboratories, Murray Hill, NJ, Oct 1963. (See A001883)
  • N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
  • N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Crossrefs

Third column of A080061.
Cf. A001883-A001891.

Extensions

More terms from Vladeta Jovovic, Vladimir Baltic, Jan 23 2003
a(21)-a(23) from Vaclav Kotesovec, Oct 10 2017

A104734 Triangle T(n,k) = sum_{j=k..n} (2n-2j+1)*binomial(k,j-k), read by rows, 0<=k<=n.

Original entry on oeis.org

1, 3, 1, 5, 4, 1, 7, 8, 5, 1, 9, 12, 12, 6, 1, 11, 16, 20, 17, 7, 1, 13, 20, 28, 32, 23, 8, 1, 15, 24, 36, 48, 49, 30, 9, 1, 17, 28, 44, 64, 80, 72, 38, 10, 1, 19, 32, 52, 80, 112, 129, 102, 47, 11, 1, 21, 36, 60, 96, 144, 192, 201, 140, 57, 12, 1, 23, 40, 68, 112, 176, 256, 321, 303, 187, 68, 13, 1, 25, 44, 76, 128, 208, 320, 448, 522, 443, 244, 80, 14, 1
Offset: 0

Views

Author

Gary W. Adamson, Mar 20 2005

Keywords

Comments

Array A210489 (without first row) read downwards antidiagonals. - R. J. Mathar, Sep 17 2013

Examples

			First few rows of the triangle are:
1;
3, 1;
5, 4, 1;
7, 8, 5, 1;
9, 12, 12, 6, 1;
11, 16, 20, 17, 7, 1;
...

Crossrefs

Cf. A001891 (row sums), A026729.

Formula

Matrix product of the triangle A = A099375 by B = [1; 0, 1; 0, 1, 1; 0, 0, 2, 1; 0, 0, 1, 3, 1;...] (which is the triangular view of A026729).

A152203 Triangle T(n,k) = (2n+1-2k)*fibonacci(k), read by rows.

Original entry on oeis.org

1, 3, 1, 5, 3, 2, 7, 5, 6, 3, 9, 7, 10, 9, 5, 11, 9, 14, 15, 15, 8, 13, 11, 18, 21, 25, 24, 13, 15, 13, 22, 27, 35, 40, 39, 21, 17, 15, 26, 33, 45, 56, 65, 63, 34, 19, 17, 30, 39, 55, 72, 91, 105, 102, 55, 21, 19, 34, 45, 65, 88, 117, 147, 170, 165
Offset: 1

Views

Author

Gary W. Adamson, Nov 29 2008

Keywords

Examples

			First few rows of the triangle =
1;
3, 1;
5, 3, 2;
7, 5, 6, 3;
9, 7, 10, 9, 5;
11, 9, 14, 15, 15, 8;
13, 11, 18, 21, 25, 24, 13;
15, 13, 22, 27, 35, 40, 39, 21;
17, 15, 26, 33, 45, 56, 65, 63, 34;
...
Row 4 = (7, 5, 6, 3) = termwise products of (7, 5, 3, 1) and (1, 1, 2, 3).

Crossrefs

Cf. A099375, A127647, A001891 (row sums).

Programs

  • Mathematica
    Flatten[Table[(2n+1-2k)Fibonacci[k],{n,15},{k,n}]] (* Harvey P. Dale, Mar 15 2015 *)

Formula

Triangle read by rows, A099375 * A127647 = termwise products of odd numbers and the Fibonacci series.
Previous Showing 31-35 of 35 results.

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

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