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.

A153372 Number of zig-zag paths from top to bottom of a rectangle of width 11 with 2n-1 rows whose color is that of the top right corner.

Original entry on oeis.org

6, 20, 72, 264, 976, 3624, 13488, 50264, 187440, 699240, 2609008, 9735768, 36332016, 135588200, 506012592, 1888445784, 7047737776, 26302439784, 98161890288, 366344859224, 1367217022320, 5102522181480, 19042869606448
Offset: 1

Views

Author

Joseph Myers, Dec 24 2008

Keywords

Links

Crossrefs

A153368, A153369, A153370, A153371, A153373

Formula

Empirical g.f. -2*x*(3-8*x+3*x^2) / ( (2*x-1)*(x^2-4*x+1) ) with a(n)= +6*a(n-1) -9*a(n-2) +2*a(n-3) and a(n) = (2^n+8*A001075(n))/3. - R. J. Mathar, Jun 16 2011

A153373 Number of zig-zag paths from top to bottom of a rectangle of width 11 with 2n-1 rows whose color is not that of the top right corner.

Original entry on oeis.org

5, 18, 66, 244, 906, 3372, 12566, 46860, 174810, 652252, 2433942, 9083004, 33897050, 126503148, 472111446, 1761934444, 6575609946, 24540472572, 91586214806, 341804255580, 1275630545370, 4760717401612, 17767238012502
Offset: 1

Views

Author

Joseph Myers, Dec 24 2008

Keywords

Links

Crossrefs

Cf. A153368-A153372.

Formula

Empirical G.f.: x*(5-12*x+3*x^2)/(1-6*x+9*x^2-2*x^3). - Colin Barker, Jan 04 2012

A153369 Number of zig-zag paths from top to bottom of a rectangle of width 11 with n rows whose color is that of the top right corner.

Original entry on oeis.org

6, 10, 20, 36, 72, 132, 264, 488, 976, 1812, 3624, 6744, 13488, 25132, 50264, 93720, 187440, 349620, 699240, 1304504, 2609008, 4867884, 9735768, 18166008, 36332016, 67794100, 135588200, 253006296, 506012592, 944222892, 1888445784, 3523868888
Offset: 1

Views

Author

Joseph Myers, Dec 24 2008

Keywords

Links

Crossrefs

A153368, A153370, A153371, A153372, A153373

Programs

  • Mathematica
    LinearRecurrence[{0,6,0,-9,0,2},{6,10,20,36,72,132},40] (* Harvey P. Dale, Sep 25 2024 *)

Formula

Empirically, g.f. -2*x*(3+5*x-8*x^2-12*x^3+3*x^4+3*x^5) / ( (2*x^2-1)*(x^4-4*x^2+1) ) with a(n)= +6*a(n-2) -9*a(n-4) +2*a(n-6). - R. J. Mathar, Jun 16 2011

A153370 Number of zig-zag paths from top to bottom of a rectangle of width 11 with n rows whose color is not that of the top right corner.

Original entry on oeis.org

5, 10, 18, 36, 66, 132, 244, 488, 906, 1812, 3372, 6744, 12566, 25132, 46860, 93720, 174810, 349620, 652252, 1304504, 2433942, 4867884, 9083004, 18166008, 33897050, 67794100, 126503148, 253006296, 472111446, 944222892, 1761934444, 3523868888
Offset: 1

Views

Author

Joseph Myers, Dec 24 2008

Keywords

Links

Crossrefs

A153368, A153369, A153372. Bisections: A153371, A153373.

Formula

Empirical: G.f. -x*(2*x+1)*(3*x^4-12*x^2+5) / ( (2*x^2-1)*(x^4-4*x^2+1) ) and a(n)= +6*a(n-2) -9*a(n-4) +2*a(n-6). - R. J. Mathar, Jun 16 2011

A153371 Number of zig-zag paths from top to bottom of a rectangle of width 11 with 2n rows whose color is that of the top right corner.

Original entry on oeis.org

10, 36, 132, 488, 1812, 6744, 25132, 93720, 349620, 1304504, 4867884, 18166008, 67794100, 253006296, 944222892, 3523868888, 13151219892, 49080945144, 183172429612, 683608511160, 2551261090740, 9521434803224, 35534476025004
Offset: 1

Views

Author

Joseph Myers, Dec 24 2008

Keywords

Links

Crossrefs

A153368, A153369, A153370, A153372, A153373

Formula

Empirical: G.f. -2*x*(5-12*x+3*x^2) / ( (2*x-1)*(x^2-4*x+1) ) with a(n)= +6*a(n-1) -9*a(n-2) +2*a(n-3) and a(n) = (2^n+4*A001075(n+1))/3. - R. J. Mathar, Jun 16 2011
Showing 1-5 of 5 results.

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

Content is available under The OEIS End-User License Agreement.