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.

A095696 T(n,5) diagonal of triangle in A095693.

Original entry on oeis.org

22, 822, 8547, 52892, 238392, 863289, 2660889, 7245414, 17879004, 40719679, 86762676, 174750576, 335401976, 617395086, 1095642486, 1882507308, 3142740258, 5113062108, 8127478513, 12649594188, 19313392560, 28974165935, 42771520935, 62206645410, 89236307160
Offset: 5

Views

Author

Nicholas S. Horne (nickhorne(AT)cox.net), Jul 06 2004

Keywords

References

  • Nicholas S. Horne, "Analysis of Viable Network Configurations from a Combinatorial, Graphical and Algebraic Perspective." Diss. Providence College, 2004.

Links

Programs

  • Mathematica
    LinearRecurrence[{11,-55,165,-330,462,-462,330,-165,55,-11,1},{22,822,8547,52892,238392,863289,2660889,7245414,17879004,40719679,86762676},30] (* Harvey P. Dale, Sep 10 2021 *)

Formula

a(n) = ((n)(n-1)(n-2)(n-3)(n-4)(n^5+5n^4+45n^3-1605n^2+9234n-17216))/3840.
G.f.: x^5*(22+580*x+715*x^2+455*x^3-1705*x^4+878*x^5)/(1-x)^11. [Colin Barker, Jun 25 2012]

A095694 T(n,3) diagonal of triangle in A095693.

Original entry on oeis.org

1, 22, 130, 485, 1400, 3416, 7392, 14610, 26895, 46750, 77506, 123487, 190190, 284480, 414800, 591396, 826557, 1134870, 1533490, 2042425, 2684836, 3487352, 4480400, 5698550, 7180875, 8971326, 11119122, 13679155, 16712410, 20286400, 24475616, 29361992, 35035385, 41594070, 49145250
Offset: 2

Views

Author

Nicholas S. Horne (nickhorne(AT)cox.net), Jul 06 2004

Keywords

References

  • Nicholas S. Horne, Analysis of Viable Network Configurations from a Combinatorial, Graphical and Algebraic Perspective, Diss. Providence College, 2004.

Links

Crossrefs

Cf. A095693.

Programs

  • Mathematica
    LinearRecurrence[{7,-21,35,-35,21,-7,1},{1,22,130,485,1400,3416,7392},30] (* Harvey P. Dale, Jul 10 2021 *)

Formula

a(n) = (n + 1)*n*(n - 1)*(n^3 + 3*n^2 + 2*n - 16)/48. - corrected by Eric Rowland, Aug 15 2017
G.f.: x^2*(2*x^3-3*x^2+15*x+1)/(1-x)^7. - Colin Barker, Nov 24 2012
a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7). - Wesley Ivan Hurt, Apr 12 2023

A095695 T(n,4) diagonal of triangle in A095693.

Original entry on oeis.org

6, 130, 1005, 4830, 17465, 52101, 135135, 314985, 674685, 1349205, 2548546, 4587765, 7925190, 13210190, 21341970, 33540966, 51434520, 77158620, 113477595, 163923760, 232959111, 326161275, 450436025
Offset: 4

Views

Author

Nicholas S. Horne (nickhorne(AT)cox.net), Jul 06 2004

Keywords

References

  • Nicholas S. Horne, Analysis of Viable Network Configurations from a Combinatorial, Graphical and Algebraic Perspective, Diss. Providence College, 2004.

Links

Formula

a(n) = n*(n-1)*(n-2)*(n-3)*(n^4+2*n^3-13*n^2-54*n+136)/384.
G.f.: -x^4*(11*x^4-39*x^3+51*x^2+76*x+6)/(x-1)^9. - Colin Barker, Nov 24 2012
Showing 1-3 of 3 results.

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

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