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.

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A225419 Triangle read by rows: T(n,k) (0 <= k <= n) = binomial(2*n+2,k).

Original entry on oeis.org

1, 1, 4, 1, 6, 15, 1, 8, 28, 56, 1, 10, 45, 120, 210, 1, 12, 66, 220, 495, 792, 1, 14, 91, 364, 1001, 2002, 3003, 1, 16, 120, 560, 1820, 4368, 8008, 11440, 1, 18, 153, 816, 3060, 8568, 18564, 31824, 43758, 1, 20, 190
Offset: 0

Views

Author

Roger L. Bagula, May 07 2013

Keywords

Comments

Row sums are A000346.

Examples

			Triangle begins:
1,
1, 4,
1, 6, 15,
1, 8, 28, 56,
1, 10, 45, 120, 210,
1, 12, 66, 220, 495, 792,
1, 14, 91, 364, 1001, 2002, 3003,
...

Links

Crossrefs

Cf. A127673, A062344, A034870, A000346.

Programs

  • Mathematica
    Flatten[Table[Table[DifferenceRoot[Function[{y, n}, {(-(2*m + 1) + n) y[n] + n y[1 + n] == 0, y[1] == 1}]][k], {k, 1, m}], {m, 1, 10}]]
Flatten[Table[Binomial[2n+2,k],{n,0,10},{k,0,n}]] (* Harvey P. Dale, Apr 13 2014 *)

Extensions

Edited by N. J. A. Sloane, May 11 2013

A261365 Prime-numbered rows of Pascal's triangle.

Original entry on oeis.org

1, 2, 1, 1, 3, 3, 1, 1, 5, 10, 10, 5, 1, 1, 7, 21, 35, 35, 21, 7, 1, 1, 11, 55, 165, 330, 462, 462, 330, 165, 55, 11, 1, 1, 13, 78, 286, 715, 1287, 1716, 1716, 1287, 715, 286, 78, 13, 1, 1, 17, 136, 680, 2380, 6188, 12376, 19448, 24310, 24310, 19448, 12376, 6188, 2380, 680, 136, 17, 1, 1, 19, 171, 969, 3876, 11628, 27132, 50388, 75582, 92378, 92378, 75582, 50388, 27132, 11628, 3876, 969, 171, 19, 1
Offset: 1

Views

Author

Maghraoui Abdelkader, Aug 16 2015

Keywords

Examples

			1,2,1;
1,3,3,1;
1,5,10,10,5,1;
1,7,21,35,35,21,7,1;
1,11,55,165,330,462,462,330,165,55,11,1;

Links

Crossrefs

Cf. A007318, A034870, A034871.
Cf. A000040 (2nd column), A008837 (3rd column).

Programs

  • Mathematica
    Table[Binomial[Prime@ n, k], {n, 8}, {k, 0, Prime@ n}] // Flatten (* Michael De Vlieger, Aug 20 2015 *)
  • PARI
    forprime(n=2, 20, for(k=0,n,print1(binomial(n,k),", ")))

Formula

T(n,k) = binomial(prime(n), k).

A261507 Fibonacci-numbered rows of Pascal's triangle. Triangle read by rows: T(n,k)= binomial(Fibonacci(n), k).

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 5, 10, 10, 5, 1, 1, 8, 28, 56, 70, 56, 28, 8, 1, 1, 13, 78, 286, 715, 1287, 1716, 1716, 1287, 715, 286, 78, 13, 1, 1, 21, 210, 1330, 5985, 20349, 54264, 116280, 203490, 293930, 352716, 352716, 293930, 203490, 116280, 54264, 20349, 5985, 1330, 210, 21, 1
Offset: 0

Views

Author

Maghraoui Abdelkader, Aug 22 2015

Keywords

Comments

Subsequence of A007318.

Examples

			1,
1,  1,
1,  1,
1,  2,  1,
1,  3,  3,   1,
1,  5, 10,  10,   5,    1,
1,  8, 28,  56,  70,   56,   28,    8,    1,
1, 13, 78, 286, 715, 1287, 1716, 1716, 1287, 715, 286, 78, 13, 1

Links

Crossrefs

Cf. A000045, A007318.
Cf. A036355, A037027, A228074, A162741, A034871, A034870, A191797.

Programs

  • Mathematica
    Table[Binomial[Fibonacci[n], k], {n, 0, 8}, {k, 0, Fibonacci[n]}]//Flatten (* Jean-François Alcover, Nov 12 2015*)
  • PARI
    v = vector(101,j,fibonacci(j)); i=0; n=0; while(n<100, for(k=0, n, print1(binomial(n, k), ", ","")); print(); i=i+1; n=v[i] ;)

Formula

T(n, k) = binomial(fibonacci(n), k).
T(n, 1) = fibonacci(n) = A000045(n).
T(n, 2) = A191797(n) for n>3.
Previous Showing 21-23 of 23 results.

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

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