|
Search: id:A087218
|
|
|
| A087218 |
|
Satisfies A(x) = 1 + x*A(x)*f(x)^2, where f(x)=sum(k>=0,x^((3^n-1)/2)) and f(x)^2 = 2 - f(x^2) + 2*sum(n>0, x^A023745(n)). |
|
+0
3
|
|
| 1, 1, 3, 6, 13, 30, 66, 147, 327, 726, 1614, 3588, 7974, 17725, 39399, 87573, 194655, 432669, 961716, 2137659, 4751490, 10561392, 23475378, 52179987, 115983270, 257802273, 573031011, 1273706934, 2831137095, 6292921101, 13987615113
(list; graph; listen)
|
|
|
OFFSET
|
0,3
|
|
|
FORMULA
|
a(n)=A078932(2n). a(m)=1 (mod 3) when m=(3^n-1)/2, otherwise a(m)=0 (mod 3).
|
|
EXAMPLE
|
Given f(x) = 1 +x +x^4 +x^13 +x^40 +x^121 +... so that f(x)^2 = 1 +2x +x^2 +2x^4 +2x^5 +x^8 +2*x^13 +... then A(x) = 1 + x*A(x)*(1 +2x +x^2 +2x^4 +2x^5 +x^8 +...) = 1 +x +3x^2 +6x^3 +13x^4 +30x^5 +...
|
|
PROGRAM
|
(PARI) a(n)=local(A, m); if(n<1, 1, m=1; A=1+O(x); while(m<=2*n, m*=3; A=1/(1/subst(A, x, x^3)-x)); polcoeff(A, 2*n));
|
|
CROSSREFS
|
Cf. A078932, A023745, A087219.
Adjacent sequences: A087215 A087216 A087217 this_sequence A087219 A087220 A087221
Sequence in context: A093128 A005313 A108639 this_sequence A098075 A137584 A125267
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Paul D. Hanna (pauldhanna(AT)juno.com), Aug 26 2003
|
|
|
Search completed in 0.002 seconds
|
