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.

A302603 Number of total dominating sets in the wheel graph on n nodes.

Original entry on oeis.org

4, 2, 4, 11, 24, 42, 79, 156, 304, 587, 1144, 2246, 4419, 8712, 17224, 34131, 67744, 134642, 267919, 533636, 1063704, 2121627, 4233904, 8452686, 16880899, 33722192, 67380304, 134656931, 269146104, 538020762, 1075602319, 2150493996, 4299838144, 8597815787
Offset: 1

Views

Author

Eric W. Weisstein, Apr 10 2018

Keywords

Comments

Extended to a(1)-a(3) using the formula/recurrence.

Programs

  • Mathematica
    Table[LucasL[n - 1] + 2 Sin[n Pi/2] + 2^(n - 1) - 1, {n, 20}]
    LinearRecurrence[{4, -5, 3, -2, -1, 2}, {4, 2, 4, 11, 24, 42}, 20]
    CoefficientList[Series[(-4 + 14 x - 16 x^2 + 7 x^3 - 2 x^4 + 3 x^5)/(-1 + 4 x - 5 x^2 + 3 x^3 - 2 x^4 - x^5 + 2 x^6), {x, 0, 20}], x]

Formula

a(n) = A000032(n - 1) + 2*sin(n*Pi/2) + 2^(n - 1) - 1.
a(n) = 4*a(n-1) - 5*a(n-2) + 3*a(n-3) - 2*a(n-4) - a(n-5) + 2*a(n-6).
G.f.: x*(-4+14*x-16*x^2+7*x^3+3*x^5-2*x^4) / ( (x-1)*(2*x-1)*(x^2+x-1)*(x^2+1) ).