|
| |
|
|
A115792
|
|
A dihedial D1 elliptical transform on A000073.
|
|
0
|
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
2,5
|
|
|
COMMENTS
|
D1 elliptical invariant transform leaves the ratio unchanged.
|
|
|
LINKS
|
|
|
|
FORMULA
|
a(n) = -floor(g(A000073(n))) with g(k) = (k-1)^2/(-4*k).
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
|
|
|
|
KEYWORD
|
nonn,uned
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
