|
|
A212346
|
|
Sequence of coefficients of x^0 in marked mesh pattern generating function Q_{n,132}^(0,4,0,0)(x).
|
|
2
|
|
|
1, 1, 2, 5, 14, 28, 48, 75, 110, 154, 208, 273, 350, 440, 544, 663, 798, 950, 1120, 1309, 1518, 1748, 2000, 2275, 2574, 2898, 3248, 3625, 4030, 4464, 4928, 5423, 5950, 6510, 7104, 7733
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
COMMENTS
|
Conjecture stated in Formula holds through a(35).
|
|
LINKS
|
|
|
FORMULA
|
Conjecture: this appears to equal (n+3)(n^2-4)/6 for n >= 3, see A129936.
a(n) = 4*a(n-1)-6*a(n-2)+4*a(n-3)-a(n-4) for n>6.
G.f.: (2*x^6-5*x^5+3*x^4-x^3+4*x^2-3*x+1) / (x-1)^4.
(End)
|
|
MATHEMATICA
|
QQ0[t, x] = (1 - (1-4*x*t)^(1/2)) / (2*x*t); QQ1[t, x] = 1/(1 - t*QQ0[t, x]); QQ2[t, x] = (1 + t*(QQ1[t, x] - QQ0[t, x]))/(1 - t*QQ0[t, x]); QQ3[t, x] = (1 + t*(QQ2[t, x] - QQ0[t, x] + t*(QQ1[t, x] - QQ0[t, x])))/(1 - t*QQ0[t, x]); QQ4[t, x] = (1 + t*(QQ3[t, x] - QQ0[t, x] + t*(QQ2[t, x] - QQ0[t, x]) + (2*t^2*(QQ1[t, x] - QQ0[t, x]))))/(1 - t*QQ0[t, x]); q=Simplify[Series[QQ4[t, x], {t, 0, 35}]]; CoefficientList[q /. x -> 0, t] (* Robert Price, Jun 04 2012 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,more
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|