|
|
A192304
|
|
0-sequence of reduction of (2n-1) by x^2 -> x+1.
|
|
3
|
|
|
1, 1, 6, 13, 31, 64, 129, 249, 470, 869, 1583, 2848, 5073, 8961, 15718, 27405, 47535, 82080, 141169, 241945, 413366, 704261, 1196831, 2029248, 3433441, 5798209, 9774534, 16451149, 27646975, 46397824
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,3
|
|
COMMENTS
|
See A192232 for definition of "k-sequence of reduction of [sequence] by [substitution]".
|
|
LINKS
|
|
|
FORMULA
|
Empirical G.f.: x*(1-2*x+4*x^2-x^3)/(1-3*x+x^2+3*x^3-x^4-x^5). [Colin Barker, Feb 08 2012]
|
|
MATHEMATICA
|
c[n_] := 2 n - 1; (* odd numbers, A005408 *)
Table[c[n], {n, 1, 15}]
q[x_] := x + 1;
p[0, x_] := 1; p[n_, x_] := p[n - 1, x] + (x^n)*c[n + 1]
reductionRules = {x^y_?EvenQ -> q[x]^(y/2),
x^y_?OddQ -> x q[x]^((y - 1)/2)};
t = Table[
Last[Most[
FixedPointList[Expand[#1 /. reductionRules] &, p[n, x]]]], {n, 0,
30}]
Table[Coefficient[Part[t, n], x, 0], {n, 1, 30}] (* A192304 *)
Table[Coefficient[Part[t, n], x, 1], {n, 1, 30}] (* A178525 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|