|
Search: id:A147880
|
|
|
| A147880 |
|
A Fernandez-type expansion for Mallow's A005229: p(x,n)=Product[x+A005229[n],{n,0,Infinity}]; a(n)=Coefficients[(p(x,n)). |
|
+0
1
|
|
| 1, 1, 1, 3, 5, 8, 12, 21, 30, 50, 75, 110, 169, 249, 361, 539, 757, 1076, 1583, 2207, 3121, 4415, 6184, 8468, 11775, 16274, 22314, 30601, 41745, 56412, 77008, 103507, 138383, 186928, 249855, 333375, 443898, 588402, 778276, 1031126, 1356945, 1780645
(list; graph; listen)
|
|
|
OFFSET
|
0,4
|
|
|
COMMENT
|
The resulting polynomial is equivalent to and 1/q(x) type expansion of q(x)=x^n*f(1/x) and that expansion has a limiting ratio ( largest positive root) near:1.225067086465817 or smaller
|
|
FORMULA
|
p(x,n)=Product[x+A005229[n],{n,0,Infinity}]; a(n)=Coefficients[(p(x,n)).
|
|
MATHEMATICA
|
(*A005229*) f[n_Integer?Positive] := f[n] = f[ f[n - 2]] + f[n - f[n - 2]]; f[0] = 0; f[1] = f[2] = 1; P[x_, n_] := P[x, n] = Product[1 + f[m] *x^m, {m, 0, n}]; a2 = CoefficientList[ExpandAll[P[x, 100]], x]; Table[a2[[n]], {n, 1, 100}]
|
|
CROSSREFS
|
A005229, A147559, A147654, A147655, A004001, A147665
Sequence in context: A004398 A055606 A147879 this_sequence A020643 A092360 A129141
Adjacent sequences: A147877 A147878 A147879 this_sequence A147881 A147882 A147883
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Nov 16 2008
|
|
|
Search completed in 0.002 seconds
|
