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 1-5 of 5 results.

A103473 Number of polyominoes consisting of 7 regular unit n-gons.

Original entry on oeis.org

24, 108, 551, 333, 558, 1605, 4418, 8350, 17507, 13512, 17775, 30467, 55264, 83252, 134422, 112514, 135175, 195122, 294091, 397852, 566007, 495773, 568602, 751172, 1031920, 1307384, 1729686, 1557663, 1737915, 2169846, 2808616, 3413064
Offset: 3

Views

Author

Sascha Kurz, Feb 07 2005

Keywords

Examples

			a(3)=24 because there are 24 polyiamonds consisting of 7 triangles and a(4)=108 because there are 108 polyominoes consisting of 7 squares.

Links

Crossrefs

Cf. A103469, A103470, A103471, A103472.
Cf. A000577, A000104, A000228, A103465, A103466, A103467, A103468, A103469, A103470, A103471, A103472, A115071, A120102, A120103, A120104.

Extensions

More terms from Sascha Kurz, Jun 09 2006

A103468 Number of polyominoes consisting of n regular unit 10-gons.

Original entry on oeis.org

1, 1, 4, 19, 127, 985, 8350, 73675, 664411, 6078768, 56198759, 523924389, 4918127659
Offset: 1

Views

Author

Sascha Kurz, Feb 07 2005

Keywords

Links

Crossrefs

Cf. A000577, A000104, A000228, A103465 - A103473, A115071, A120102 - A120104.

Extensions

More terms from Sascha Kurz, Jun 09 2006

A103466 Number of polyominoes consisting of n regular unit octagons.

Original entry on oeis.org

1, 1, 3, 11, 50, 269, 1605, 10102, 65323, 430302, 2868320, 19299334, 130807068, 892075515, 6115673262
Offset: 1

Views

Author

Sascha Kurz, Feb 07 2005

Keywords

Links

Crossrefs

Cf. A000577, A000104, A000228, A103465, A103465, A103467, A103468.
Cf. A000577, A000104, A000228, A103465, A103467, A103468, A103469, A103470, A103471, A103472, A103473, A115071, A120102, A120103, A120104.

Extensions

More terms from Sascha Kurz, Jun 09 2006
Definition corrected by John Mason and Sascha Kurz, Sep 20 2020

A103467 Number of polyominoes consisting of n regular unit 9-gons.

Original entry on oeis.org

1, 1, 3, 14, 82, 585, 4418, 34838, 280014, 2285047, 18838395, 156644526, 1311575691
Offset: 1

Views

Author

Sascha Kurz, Feb 07 2005

Keywords

Links

Crossrefs

Cf. A000577, A000104, A000228, A103465, A103466, A103468, A103469, A103470, A103471, A103472, A103473, A115071, A120102, A120103, A120104.

Extensions

More terms from Sascha Kurz, Jun 09 2006
Definition corrected by John Mason and Sascha Kurz, Sep 20 2020

A120487 Denominator of 1^n/n + 2^n/(n-1) + 3^n/(n-2) + ... + (n-1)^n/2 + n^n/1.

Original entry on oeis.org

1, 2, 3, 12, 5, 20, 35, 280, 63, 2520, 385, 27720, 6435, 8008, 45045, 720720, 85085, 4084080, 969969, 739024, 29393, 5173168, 7436429, 356948592, 42902475, 2974571600, 717084225, 80313433200, 215656441, 2329089562800, 4512611027925
Offset: 1

Views

Author

Alexander Adamchuk, Jul 22 2006

Keywords

Comments

Numerator is A115071(n).
Also a(n) is denominator of (n+1)^(n+1) * (H(n+1) - 1), where H(k) is harmonic number, H(k) = Sum_{i=1..k} 1/i = A001008(k)/A002805(k). - Alexander Adamchuk, Jan 02 2007

Crossrefs

Cf. A115071, A027612, A031971, A002805.
Cf. A001008, A002805.

Programs

  • Mathematica
    Denominator[Table[Sum[k^n/(n-k+1),{k,1,n}],{n,1,50}]]
Table[ Denominator[ (n+1)^(n+1) * Sum[ 1/i,{i,2,n+1} ] ], {n,1,40} ] (* Alexander Adamchuk, Jan 02 2007 *)

Formula

a(n) = denominator(Sum_{k=1..n} k^n/(n-k+1)).
a(n) = denominator((n+1)^(n+1) * Sum_{i=2..n+1} 1/i). - Alexander Adamchuk, Jan 02 2007
Showing 1-5 of 5 results.

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