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.

A245739 Decimal expansion of z_kag, the bulk limit of the number of spanning trees on a kagomé lattice.

Original entry on oeis.org

1, 1, 3, 5, 6, 9, 6, 4, 0, 1, 7, 7, 5, 1, 0, 2, 5, 2, 3, 7, 6, 0, 2, 1, 9, 9, 7, 0, 6, 6, 6, 5, 7, 8, 0, 8, 1, 0, 2, 8, 0, 6, 6, 6, 3, 2, 0, 2, 8, 6, 4, 6, 5, 9, 5, 5, 0, 3, 2, 3, 8, 8, 9, 8, 3, 1, 1, 9, 8, 7, 8, 2, 6, 4, 0, 8, 2, 1, 7, 6, 3, 0, 9, 6, 6, 1, 3, 9, 0, 4, 2, 4, 1, 9, 0, 0, 2, 5, 7, 8, 8, 9, 9
Offset: 1

Views

Author

Jean-François Alcover, Jul 31 2014

Keywords

Examples

			1.1356964017751025237602199706665780810280666320286465955...

Links

Crossrefs

Cf. A218387(z_sq), A242967(H), A245725(z_tri), A245736(z_br), A245737(z_hc).

Programs

  • Mathematica
    H = Sqrt[3]/(6*Pi)*PolyGamma[1, 1/6] - Pi/Sqrt[3] - Log[6]; RealDigits[(1/3)*(2*Log[2] + 2*Log[3] + H), 10, 103] // First

Formula

(1/3)*(2*log(2) + 2*log(3) + H), where H is the auxiliary constant A242967.
Equals (1/3)*(A245725 + log(6)).

A245740 Decimal expansion of z_(3-12-12), the bulk limit of the number of spanning trees on a 3-12-12 lattice.

Original entry on oeis.org

7, 2, 0, 5, 6, 3, 3, 2, 2, 8, 6, 6, 5, 7, 7, 1, 0, 6, 0, 7, 7, 3, 6, 4, 5, 2, 0, 6, 2, 7, 9, 5, 7, 5, 5, 2, 4, 2, 2, 3, 8, 3, 5, 1, 9, 3, 3, 2, 3, 6, 7, 0, 4, 2, 3, 8, 3, 6, 1, 4, 0, 9, 6, 1, 5, 2, 7, 9, 1, 4, 7, 4, 1, 6, 0, 4, 3, 5, 9, 9, 0, 3, 2, 0, 4, 4, 7, 9, 4, 6, 3, 9, 2, 2, 9, 4, 7, 7, 6, 6, 5, 9, 2
Offset: 0

Views

Author

Jean-François Alcover, Jul 31 2014

Keywords

Examples

			0.720563322866577106077364520627957552422383519332367042383614...

Links

Crossrefs

Cf. A218387(z_sq), A242967(H), A245725(z_tri), A245736(z_br), A245737(z_hc), A245739(z_kag).

Programs

  • Mathematica
    H = Sqrt[3]/(6*Pi)*PolyGamma[1, 1/6] - Pi/Sqrt[3] - Log[6]; RealDigits[(1/6)*(Log[2] + 2*Log[3] + Log[5] + H), 10, 103] // First

Formula

(1/6)*(log(2) + 2*log(3) + log(5) + H), where H is the auxiliary constant A242967.
Equals (1/6)*(A245725 + log(15)).

A245741 Decimal expansion of z_UJ, the bulk limit of the number of spanning trees on a Union Jack lattice.

Original entry on oeis.org

1, 5, 7, 3, 3, 6, 8, 5, 5, 0, 7, 5, 7, 6, 6, 4, 3, 5, 8, 2, 4, 3, 3, 1, 5, 9, 7, 8, 9, 8, 9, 3, 9, 0, 7, 6, 1, 1, 0, 2, 3, 4, 1, 6, 3, 3, 1, 5, 6, 0, 6, 5, 4, 9, 9, 4, 3, 7, 2, 9, 2, 9, 0, 3, 7, 9, 7, 6, 3, 5, 9, 8, 5, 7, 6, 3, 6, 7, 9, 8, 7, 4, 4, 8, 7, 9, 3, 7, 3, 3, 4, 5, 2, 3, 0, 4, 6, 9, 5, 6, 1, 9, 1, 6
Offset: 1

Views

Author

Jean-François Alcover, Jul 31 2014

Keywords

Examples

			1.5733685507576643582433159789893907611023416331560654994372929...

Links

Crossrefs

Cf. A218387(z_sq), A245725(z_tri), A245736(z_br), A245737(z_hc), A245739(z_kag), A245740(z_(3-12-12)).

Programs

  • Mathematica
    z[UJ] = 2*Catalan/Pi + (1/2)*Log[3 - 2*Sqrt[2]] + (2/Pi)*Integrate[ArcTan[t]/t, {t, 0, 3 + 2*Sqrt[2]}]; RealDigits[N[Re[z[UJ]], 104]] // First

Formula

2*C/Pi + (1/2)*log(3-2*sqrt(2)) + (2/Pi)*integral_{0..3+2*sqrt(2)} arctan(t)/t dt, where C is Catalan's constant.
Equals 2*A245736.
Showing 1-3 of 3 results.

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