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 1-2 of 2 results.

A384672 Expansion of (1+2*x-x^2) / (1-2*x-5*x^2+2*x^3).

Original entry on oeis.org

1, 4, 12, 42, 136, 458, 1512, 5042, 16728, 55642, 184840, 614434, 2041784, 6786058, 22552168, 74951058, 249090840, 827832634, 2751217352, 9143416194, 30387253880, 100989154026, 335627745064, 1115426752498, 3707013922264, 12319906116890, 40944028340104
Offset: 0

Views

Author

Sean A. Irvine, Jun 05 2025

Keywords

Comments

Number of walks of length n starting at vertex 1 in the following graph:
1---2
/|\ /|
0 | X |
\|/ \|
4---3.
Also, by symmetry, the number of walks of length n starting at 4 in the same graph.

Examples

			a(2)=12 because we have the walks 1-0-1, 1-0-4, 1-2-1, 1-2-3, 1-2-4, 1-3-1, 1-3-2, 1-3-4, 1-4-0, 1-4-1, 1-4-2, 1-4-3.

Links

Crossrefs

Cf. A384671 (vertex 0), A384673 (vertices 2 and 3), A384646 (missing edge {2,4}).

Programs

  • Maple
    a:= n-> (<<0|1|0|0|1>, <1|0|1|1|1>, <0|1|0|1|1>, <0|1|1|0|1>, <1|1|1|1|0>>^n. <<1,1,1,1,1>>)[2,1]:
seq(a(n), n=0..32);
  • Mathematica
    CoefficientList[Series[(1+2*x-x^2) / (1-2*x-5*x^2+2*x^3), {x, 0, 32}], x]
LinearRecurrence[{2,5,-2},{1,4,12},30] (* Harvey P. Dale, Aug 30 2025 *)

A384673 Expansion of (1+x) / (1-2*x-5*x^2+2*x^3).

Original entry on oeis.org

1, 3, 11, 35, 119, 391, 1307, 4331, 14415, 47871, 159155, 528835, 1757703, 5841271, 19413387, 64517723, 214419839, 712601519, 2368266787, 7870701491, 26157533879, 86932041639, 288910349691, 960165839819, 3191019344815, 10605047189343, 35244859423123
Offset: 0

Views

Author

Sean A. Irvine, Jun 05 2025

Keywords

Comments

Number of walks of length n starting at vertex 2 in the following graph:
1---2
/|\ /|
0 | X |
\|/ \|
4---3.
Also, by symmetry, the number of walks of length n starting at 3 in the same graph.

Examples

			a(2)=11 because we have the walks 2-1-0, 2-1-2, 2-1-3, 2-1-4, 2-3-1, 2-3-2, 2-3-4, 2-4-0, 2-4-1, 2-4-2, 2-4-3.

Links

Crossrefs

Cf. A384671 (vertex 0), A384672 (vertices 1 and 4), A384646 (missing edge {2,4}).

Programs

  • Maple
    a:= n-> (<<0|1|0|0|1>, <1|0|1|1|1>, <0|1|0|1|1>, <0|1|1|0|1>, <1|1|1|1|0>>^n. <<1,1,1,1,1>>)[3,1]:
seq(a(n), n=0..32);
  • Mathematica
    CoefficientList[Series[(1+x) / (1-2*x-5*x^2+2*x^3), {x, 0, 32}], x]
Showing 1-2 of 2 results.

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

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