A115792 A dihedial D1 elliptical transform on A000073.

0, 0, 1, 1, 2, 3, 6, 11, 20, 37, 69, 126, 232, 426, 784, 1442, 2652, 4878, 8973, 16503, 30354, 55829, 102686, 188869, 347384, 638939, 1175193, 2161516, 3975648, 7312356, 13449520, 24737524, 45499400, 83686444, 153923369, 283109213, 520719026, 957751607

Offset

2,5

Comments

D1 elliptical invariant transform leaves the ratio unchanged.

Links

Table of n, a(n) for n=2..39.

Formula

a(n) = -floor(g(A000073(n))) with g(k) = (k-1)^2/(-4*k).

Conjectures from Chai Wah Wu, Dec 21 2023: (Start)

a(n) = a(n-2) + 2*a(n-3) + 2*a(n-4) + 2*a(n-5) + 2*a(n-6) + 2*a(n-7) + 3*a(n-8) + 2*a(n-9) + a(n-10) for n > 11.

G.f.: x^4*(-x^2 - x - 1)/((x + 1)*(x^2 + 1)*(x^4 + 1)*(x^3 + x^2 + x - 1)). (End)

Mathematica

g[x_] = (x - 1)^2/(-4*x) M = {{0, 1, 0}, {0, 0, 1}, {1, 1, 1}} w[0] = {0, 1, 1}; w[n_] := w[n] = M.w[n - 1] a0 = Table[ -Floor[g[w[n][[1]]]], {n, 1, 25}] b0 = Table[N[a0[[n + 1]]/a0[[n]]], {n, 2, 24}]

Crossrefs

Cf. A000073.

Sequence in context: A001590 A078042 A047081 * A054177 A186546 A318910

Adjacent sequences: A115789 A115790 A115791 * A115793 A115794 A115795

Keyword

nonn,uned

Author

Roger L. Bagula, Mar 13 2006

Status

approved