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.

A292540 Number of 3-cycles in the n-Sierpinski tetrahedron graph.

Original entry on oeis.org

4, 20, 80, 320, 1280, 5120, 20480, 81920, 327680, 1310720, 5242880, 20971520, 83886080, 335544320, 1342177280, 5368709120, 21474836480, 85899345920, 343597383680, 1374389534720, 5497558138880, 21990232555520, 87960930222080, 351843720888320, 1407374883553280
Offset: 1

Views

Author

Eric W. Weisstein, Sep 18 2017

Keywords

Links

Crossrefs

Cf. A003947, A269696.
Cf. A292542 (4-cycles), A292543 (5-cycles), A292545 (6-cycles).

Programs

  • Mathematica
    Table[If[n == 1, 4, 5 4^(n - 1)], {n, 10}]
Join[{4}, LinearRecurrence[{4}, {20}, 30]]
CoefficientList[Series[-((4 (1 + x))/(-1 + 4 x)), {x, 0, 20}], x]
Join[{4},NestList[4#&,20,30]] (* Harvey P. Dale, Sep 21 2019 *)

Formula

a(n) = 5*4^(n - 1) for n > 1.
a(n) = 4*a(n-1) for n > 2.
G.f. -4*x*(1 + x)/(-1 + 4 x).

A292543 Number of 5-cycles in the n-Sierpinski tetrahedron graph.

Original entry on oeis.org

0, 96, 384, 1536, 6144, 24576, 98304, 393216, 1572864, 6291456, 25165824, 100663296, 402653184, 1610612736, 6442450944, 25769803776, 103079215104, 412316860416, 1649267441664, 6597069766656, 26388279066624, 105553116266496, 422212465065984, 1688849860263936
Offset: 1

Views

Author

Eric W. Weisstein, Sep 18 2017

Keywords

Links

Crossrefs

Cf. A002023 (6*4^n).
Cf. A292540 (3-cycles), A292542 (4-cycles), A292545 (6-cycles).

Programs

  • Mathematica
    Table[If[n == 1, 0, 6 4^n], {n, 20}]
Join[{0}, LinearRecurrence[{4}, {96}, 20]]
CoefficientList[Series[96 x/(1 - 4 x), {x, 0, 20}], x]

Formula

a(n) = 6*4^n = A002023(n) for n > 1.
a(n) = 4*a(n-1) for n > 2.
G.f.: 96*x^/(1 - 4*x).

A292545 Number of 6-cycles in the n-Sierpinski tetrahedron graph.

Original entry on oeis.org

0, 218, 876, 3504, 14016, 56064, 224256, 897024, 3588096, 14352384, 57409536, 229638144, 918552576, 3674210304, 14696841216, 58787364864, 235149459456, 940597837824, 3762391351296, 15049565405184, 60198261620736, 240793046482944, 963172185931776, 3852688743727104
Offset: 1

Views

Author

Eric W. Weisstein, Sep 18 2017

Keywords

Links

Crossrefs

Cf. A292540 (3-cycles), A292542 (4-cycles), A292543 (5-cycles).

Programs

  • Mathematica
    Table[Piecewise[{{0, n == 1}, {218, n == 2}}, 219 4^(n - 2)], {n, 20}]
Join[{0, 218}, LinearRecurrence[{4}, {876}, 20]]
CoefficientList[Series[-2 x (109 + 2 x)/(-1 + 4 x), {x, 0, 20}], x]
  • PARI
    concat(0, Vec(-2*x^2*(109 + 2*x)/(-1 + 4*x) + O(x^50))) \\ Michel Marcus, Sep 19 2017

Formula

a(n) = 219*4^(n - 2) for n > 2.
a(n) = 4*a(n-1) for n > 2.
G.f.: -2*x^2*(109 + 2*x)/(-1 + 4*x).
Showing 1-3 of 3 results.

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

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