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 1-10 of 21 results. Next

A069325 Number of 3 X n binary arrays with path of adjacent 1's from upper right corner to lower left corner.

Original entry on oeis.org

1, 8, 51, 295, 1632, 8830, 47239, 251261, 1332456, 7055228, 37327007, 197404203, 1043751584, 5518106750, 29171471659, 154210451661, 815197197636, 4309313949364, 22779900825195, 120418887728947
Offset: 1

Views

Author

R. H. Hardin, Mar 16 2002

Keywords

Links

Crossrefs

Row 3 of A359575.
Cf. 2 X n A048739, 4 X n A069326, 5 X n A069327, 6 X n A069328, 7 X n A069329, 8 X n A069330, 9 X n A069331, 10 X n A069332, 11 X n A069333, 12 X n A069334, 13 X n A069335, 14 X n A069336, 15 X n A069337, 16 X n A069338, 17 X n A069339, 18 X n A069340, 19 X n A069341, 20 X n A069342, n X n A069343, n X n symmetric A069344.

Programs

  • Magma
    m:=25; R:=PowerSeriesRing(Integers(), m); Coefficients(R!(x*(1-x+x^3)/((1-2*x-2*x^2)*(2*x^5-4*x^4+x^3+9*x^2-7*x+1)))); // G. C. Greubel, Apr 22 2018
  • Mathematica
    CoefficientList[Series[x*(1-x+x^3)/((1-2*x-2*x^2)*(2*x^5-4*x^4+x^3+9*x^2 -7*x+1)), {x, 0, 50}], x] (* G. C. Greubel, Apr 22 2018 *)
LinearRecurrence[{9,-21,3,24,-8,-4,4},{1,8,51,295,1632,8830,47239},20] (* Harvey P. Dale, May 21 2023 *)
  • PARI
    Vec(-x*(1-x+x^3)/(2*x^2+2*x-1)/(2*x^5-4*x^4+x^3+9*x^2-7*x+1) + O(x^99)) \\ Charles R Greathouse IV, Jun 12 2015

Formula

G.f.: x*(1-x+x^3)/((1-2*x-2*x^2)*(2*x^5-4*x^4+x^3+9*x^2-7*x+1)). - Vladeta Jovovic, Jul 02 2003

A069342 Number of 20 X n binary arrays with path of adjacent 1's from upper right corner to lower left corner.

Original entry on oeis.org

1, 27304196, 120418887728947, 273114307102338469932, 451242636516479543205804329, 625576823311351623848371148927043, 778880000189830517730349450554806038383, 903099763914081099274411192869395521423076059, 995759593882933848778575773902474323196918603122861
Offset: 1

Views

Author

R. H. Hardin, Mar 16 2002

Keywords

Crossrefs

Cf. 2 X n A048739, 3 X n A069325, 4 X n A069326, 5 X n A069327, 6 X n A069328, 7 X n A069329, 8 X n A069330, 9 X n A069331, 10 X n A069332, 11 X n A069333, 12 X n A069334, 13 X n A069335, 14 X n A069336, 15 X n A069337, 16 X n A069338, 17 X n A069339, 18 X n A069340, 19 X n A069341, n X n A069343, n X n symmetric A069344.

Extensions

a(5)-a(9) from Sean A. Irvine, Apr 28 2024

A069344 Number of n X n symmetric binary arrays with path of adjacent 1's from upper right corner to lower left corner.

Original entry on oeis.org

1, 3, 19, 246, 6486, 346550, 37410572, 8142026722, 3567024626500, 3142034178023610
Offset: 1

Views

Author

R. H. Hardin, Mar 16 2002

Keywords

Crossrefs

Cf. n X m A069325-A069342, n X n non-symmetric A069343.

A069326 Number of 4 X n binary arrays with path of adjacent 1's from upper right corner to lower left corner.

Original entry on oeis.org

1, 20, 295, 3828, 46557, 546286, 6279393, 71316632, 804230945, 9031118936, 101161197895, 1131456031256, 12643706576681, 141214773950750, 1576695869980497, 17600838146781308, 196457931325141165
Offset: 1

Views

Author

R. H. Hardin, Mar 16 2002

Keywords

Crossrefs

Row 4 of A359575.
Cf. 2 X n A048739, 3 X n A069325, 5 X n A069327, 6 X n A069328, 7 X n A069329, 8 X n A069330, 9 X n A069331, 10 X n A069332, 11 X n A069333, 12 X n A069334, 13 X n A069335, 14 X n A069336, 15 X n A069337, 16 X n A069338, 17 X n A069339, 18 X n A069340, 19 X n A069341, 20 X n A069342, n X n A069343, n X n symmetric A069344.

A069327 Number of 5 X n binary arrays with path of adjacent 1's from upper right corner to lower left corner.

Original entry on oeis.org

1, 49, 1632, 46557, 1225194, 30754544, 749866185, 17950397258, 424660442975, 9969967594443, 232909647253690, 5423397612311731, 126017939209370356, 2924071505958808678, 67786971099219351975, 1570519781573431498844
Offset: 1

Views

Author

R. H. Hardin, Mar 16 2002

Keywords

Crossrefs

Row 5 of A359575.
Cf. 2 X n A048739, 3 X n A069325, 4 X n A069326, 6 X n A069328, 7 X n A069329, 8 X n A069330, 9 X n A069331, 10 X n A069332, 11 X n A069333, 12 X n A069334, 13 X n A069335, 14 X n A069336, 15 X n A069337, 16 X n A069338, 17 X n A069339, 18 X n A069340, 19 X n A069341, 20 X n A069342, n X n A069343, n X n symmetric A069344.

A069328 Number of 6 X n binary arrays with path of adjacent 1's from upper right corner to lower left corner.

Original entry on oeis.org

1, 119, 8830, 546286, 30754544, 1636193228, 83949041929, 4204804906873, 207204257344200, 10097172081372386, 488256657363269300, 23483738804219826986, 1125283073890577118094
Offset: 1

Views

Author

R. H. Hardin, Mar 16 2002

Keywords

Crossrefs

Cf. 2 X n A048739, 3 X n A069325, 4 X n A069326, 5 X n A069327, 7 X n A069329, 8 X n A069330, 9 X n A069331, 10 X n A069332, 11 X n A069333, 12 X n A069334, 13 X n A069335, 14 X n A069336, 15 X n A069337, 16 X n A069338, 17 X n A069339, 18 X n A069340, 19 X n A069341, 20 X n A069342, n X n A069343, n X n symmetric A069344.

Extensions

a(10)-a(13) from Sean A. Irvine, Apr 27 2024

A069329 Number of 7 X n binary arrays with path of adjacent 1's from upper right corner to lower left corner.

Original entry on oeis.org

1, 288, 47239, 6279393, 749866185, 83949041929, 9009490924794, 939356338522456, 95972872569551099, 9664595615275994739, 963147644297772022870, 95261720343073832781620, 9370213923827917022436855
Offset: 1

Views

Author

R. H. Hardin, Mar 16 2002

Keywords

Crossrefs

Cf. 2 X n A048739, 3 X n A069325, 4 X n A069326, 5 X n A069327, 6 X n A069328, 8 X n A069330, 9 X n A069331, 10 X n A069332, 11 X n A069333, 12 X n A069334, 13 X n A069335, 14 X n A069336, 15 X n A069337, 16 X n A069338, 17 X n A069339, 18 X n A069340, 19 X n A069341, 20 X n A069342, n X n A069343, n X n symmetric A069344.

Extensions

a(8)-a(13) from Sean A. Irvine, Apr 27 2024

A069330 Number of 8 X n binary arrays with path of adjacent 1's from upper right corner to lower left corner.

Original entry on oeis.org

1, 696, 251261, 71316632, 17950397258, 4204804906873, 939356338522456, 203037531986079710, 42856467943438387389, 8890050748561149390768, 1820486395967688826354303, 369211160728496631061072520, 74336348859792978822695533158
Offset: 1

Views

Author

R. H. Hardin, Mar 16 2002

Keywords

Crossrefs

Cf. 2 X n A048739, 3 X n A069325, 4 X n A069326, 5 X n A069327, 6 X n A069328, 7 X n A069329, 9 X n A069331, 10 X n A069332, 11 X n A069333, 12 X n A069334, 13 X n A069335, 14 X n A069336, 15 X n A069337, 16 X n A069338, 17 X n A069339, 18 X n A069340, 19 X n A069341, 20 X n A069342, n X n A069343, n X n symmetric A069344.

Extensions

a(7)-a(13) from Sean A. Irvine, Apr 27 2024

A069331 Number of 9 X n binary arrays with path of adjacent 1's from upper right corner to lower left corner.

Original entry on oeis.org

1, 1681, 1332456, 804230945, 424660442975, 207204257344200, 95972872569551099, 42856467943438387389, 18633578769242938930634, 7941841818960714166446386, 3334133239588212397398261473, 1383615906056315517856514817504, 569069897400777230243560762294416
Offset: 1

Views

Author

R. H. Hardin, Mar 16 2002

Keywords

Crossrefs

Cf. 2 X n A048739, 3 X n A069325, 4 X n A069326, 5 X n A069327, 6 X n A069328, 7 X n A069329, 8 X n A069330, 10 X n A069332, 11 X n A069333, 12 X n A069334, 13 X n A069335, 14 X n A069336, 15 X n A069337, 16 X n A069338, 17 X n A069339, 18 X n A069340, 19 X n A069341, 20 X n A069342, n X n A069343, n X n symmetric A069344.

Extensions

a(7)-a(13) from Sean A. Irvine, Apr 27 2024

A069332 Number of 10 X n binary arrays with path of adjacent 1's from upper right corner to lower left corner.

Original entry on oeis.org

1, 4059, 7055228, 9031118936, 9969967594443, 10097172081372386, 9664595615275994739, 8890050748561149390768, 7941841818960714166446386, 6939491897974410047045467672, 5961170413774886320235399363515, 5053163560738707006885020833252029
Offset: 1

Views

Author

R. H. Hardin, Mar 16 2002

Keywords

Crossrefs

Cf. 2 X n A048739, 3 X n A069325, 4 X n A069326, 5 X n A069327, 6 X n A069328, 7 X n A069329, 8 X n A069330, 9 X n A069331, 11 X n A069333, 12 X n A069334, 13 X n A069335, 14 X n A069336, 15 X n A069337, 16 X n A069338, 17 X n A069339, 18 X n A069340, 19 X n A069341, 20 X n A069342, n X n A069343, n X n symmetric A069344.

Extensions

a(6)-a(12) from Sean A. Irvine, Apr 27 2024
Showing 1-10 of 21 results. Next

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