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 1-6 of 6 results.

A091949 a(n) = A087659(n) mod 2.

Original entry on oeis.org

1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 1, 0, 0, 1
Offset: 0

Views

Author

Benoit Cloitre, Mar 11 2004

Keywords

Programs

  • PARI
    a(n)= sum(i=0,n,2*binomial(n,i)*(n+2*i+3)!/((i+1)!*(i+2)!*(n+3)!))%2

Formula

a(n)=hypergeom([ -n, (n+4)/2, (n+5)/2], [3, 2], -4) mod 2; a(8k)=1, a(8k+1)=0, a(8k+2)=1 a(8k+3)=0, a(8k+4)=0, a(8k+5)= 035263(k+1), a(8k+6)=1-035263(k+1), a(8k+7)=A035263(k+1)

A091950 a(n) = A087659(n) mod 3.

Original entry on oeis.org

1, 0, 0, 2, 1, 1, 2, 1, 1, 1, 0, 0, 2, 1, 1, 2, 2, 2, 1, 0, 0, 2, 1, 1, 0, 0, 0, 1, 0, 0, 2, 1, 1, 2, 1, 1, 1, 0, 0, 2, 1, 1, 2, 2, 2, 1, 0, 0, 2, 1, 1, 0, 1, 1, 1, 0, 0, 2, 1, 1, 2, 1, 1, 1, 0, 0, 2, 1, 1, 2, 2, 2, 1, 0, 0, 2, 1, 1, 2, 1, 1, 1, 0, 0, 2, 1, 1, 2, 1, 1, 1, 0, 0, 2, 1, 1, 2, 2, 2, 1, 0, 0, 2, 1, 1
Offset: 0

Views

Author

Benoit Cloitre, Mar 11 2004

Keywords

Programs

  • PARI
    a(n)= sum(i=0,n,2*binomial(n,i)*(n+2*i+3)!/((i+1)!*(i+2)!*(n+3)!))%3

Formula

a(n)=hypergeom([ -n, (n+4)/2, (n+5)/2], [3, 2], -4) mod 3; a(9k)=1, a(9k+1)=0, a(9k+2)=0, a(9k+3)=2, a(9k+4)=1, a(9k+5)=1, a(9k+6)=2*A014578(k+1), a(9k+7)=z(k), a(9k+8)=z(k) where : z(9k)=1, z(9k+1)=2, z(9k+2)=0, z(9k+3)=1, z(9k+4)=2, z(9k+5)=1, z(9k+6)=1, z(9k+7)=2 and z(9k+8)=z(k).

A087662 Values of a certain hypergeometric function. Not known to be always integer-valued.

Original entry on oeis.org

5, 29, 230, 2260, 25921, 334105, 4717653, 71677935, 1156559775, 19624027967, 347486715005, 6382806114599, 121036793631550, 2360217764672530, 47174734548813698, 963862614738695410, 20085285577742751859, 426043585490101967355, 9183714902258875988330
Offset: 0

Views

Author

Bill Gosper, Sep 26 2003

Keywords

Crossrefs

Cf. A087659-A087661.

Programs

  • Mathematica
    a[n_] := 5*HypergeometricPFQ[{-n, n/2 + 7/2, n/2 + 4}, {5, 3}, -4];
Table[a[n], {n, 0, 16}] (* Jean-François Alcover, Feb 19 2018 *)

Formula

a(n) = 5*hypergeom([ -n, n/2+7/2, n/2+4], [5, 3], -4).
Recurrence: (n+4)*(n+5)*(n+6)*(3*n + 2)*a(n) = 5*(n+5)*(3*n + 4)*(6*n^2 + 14*n + 9)*a(n-1) - (n-1)*(9*n^3 + 24*n^2 + 17*n - 20)*a(n-2) + (n-4)*(n-2)*(n-1)*(3*n + 5)*a(n-3). - Vaclav Kotesovec, Jul 05 2018

Extensions

More terms from Vladeta Jovovic, Sep 30 2003

A087660 Values of a certain hypergeometric function. Not known to be always integer-valued.

Original entry on oeis.org

4, 25, 228, 2620, 35164, 527663, 8613004, 150142594, 2759219428, 52953913663, 1053779339980, 21624992868276, 455655808661008, 9823903635742978, 216106936268122100, 4839230922051864504, 110093028451517403276, 2540412583358390378215, 59374626887737992823372
Offset: 0

Views

Author

Bill Gosper, Sep 26 2003

Keywords

Crossrefs

Cf. A087659-A087662.

Programs

  • Mathematica
    a[n_] := 4*HypergeometricPFQ[{-n, (n + 5)/2, n/2 + 3}, {4, 2}, -4];
Table[a[n], {n, 0, 16}] (* Jean-François Alcover, Feb 19 2018 *)

Formula

a(n) = 4*hypergeom([ -n, n/2+5/2, n/2+3], [4, 2], -4).
Recurrence: (n+3)^2*(n+4)*(3*n - 2)*(3*n + 1)*a(n) = 10*(n+1)*(n+3)*(3*n - 2)*(3*n + 2)^2*a(n-1) - (n-1)*(n+1)*(3*n + 4)*(9*n^2 - 15*n + 14)*a(n-2) + (n-4)*(n-2)*(n-1)*(3*n + 1)*(3*n + 4)*a(n-3). - Vaclav Kotesovec, Jul 05 2018

Extensions

More terms from Vladeta Jovovic, Sep 30 2003

A087661 Values of a certain hypergeometric function. Not known to be always integer-valued.

Original entry on oeis.org

15, 99, 891, 9825, 125085, 1772775, 27303603, 449394792, 7809206685, 141975690765, 2681773580205, 52342675041564, 1051034305996356, 21635329605783960, 455225821135429270, 9766746945640199070, 213227240437260707169, 4728776305725359233781
Offset: 0

Views

Author

Bill Gosper, Sep 26 2003

Keywords

Crossrefs

Cf. A087659-A087662.

Programs

  • Mathematica
    a[n_] := 15*HypergeometricPFQ[{-n, n/2 + 3, (n + 7)/2}, {5, 2}, -4];
Table[a[n], {n, 0, 15}] (* Jean-François Alcover, Feb 19 2018 *)

Formula

a(n) = 15*hypergeom([ -n, n/2+3, n/2+7/2], [5, 2], -4).
Recurrence: (n+4)^2*(n+5)*(3*n - 1)*(3*n + 1)*(3*n + 2)*a(n) = 6*(n+4)*(3*n - 1)*(45*n^4 + 180*n^3 + 264*n^2 + 151*n + 20)*a(n-1) - 3*(n-1)*(3*n + 5)*(9*n^4 + 9*n^3 - 2*n^2 + 68*n + 16)*a(n-2) + (n-5)*(n-2)*(n-1)*(3*n + 2)*(3*n + 4)*(3*n + 5)*a(n-3). - Vaclav Kotesovec, Jul 05 2018

Extensions

More terms from Vladeta Jovovic, Sep 30 2003

A087727 Triangle read by rows: T(n,k) = (2 * (binomial(n,k)) * (n + 2 * k + 3)!)/((k + 1)! * (k + 2)! * (n + 3)!).

Original entry on oeis.org

1, 1, 5, 1, 14, 42, 1, 28, 210, 462, 1, 48, 660, 3432, 6006, 1, 75, 1650, 15015, 60060, 87516, 1, 110, 3575, 50050, 340340, 1108536, 1385670, 1, 154, 7007, 140140, 1429428, 7759752, 21339318, 23371634, 1, 208, 12740, 346528, 4938024, 39504192, 178474296, 424938800, 414315330
Offset: 0

Views

Author

Bill Gosper, Sep 30 2003

Keywords

Examples

			Triangle begins:
  1;
  1,  5;
  1, 14,  42;
  1, 28, 210, 462;
  ...

Crossrefs

Row sums give A087659. Right diagonal gives A005789.

Programs

  • PARI
    t(n, k) = (2 * (binomial(n,k)) * (n + 2*k + 3)!)/((k + 1)! * (k + 2)! * (n + 3)!) \\ Michel Marcus, Jun 26 2013

Extensions

More terms from Ray Chandler, Sep 30 2003
Showing 1-6 of 6 results.

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