A237651 - OEIS

%I #7 Oct 08 2022 07:07:22

%S 1,1,3,2,9,7,17,10,41,31,75,44,150,106,238,132,445,313,711,398,1251,

%T 853,1859,1006,3135,2129,4677,2548,7590,5042,10734,5692,16865,11173,

%U 23979,12806,36911,24105,50551,26446,75985,49539,104683,55144,155140,99996,207188,107192,300766,193574,403994

%N G.f. satisfies: A(x) = (1+x+x^2) * A(x^2)^2.

%F The odd-indexed bisection equals the self-convolution of this sequence.

%F The self-convolution cube yields A237650, the odd-indexed bisection of A195586.

%F G.f. A(x) satisfies:

%F (1) A(x) = Product_{n>=0} ( 1 + x^(2^n) + x^(2*2^n) )^(2^n).

%F (2) A(x) / A(-x) = (1+x+x^2) / (1-x+x^2).

%e G.f.: A(x) = 1 + x + 3*x^2 + 2*x^3 + 9*x^4 + 7*x^5 + 17*x^6 + 10*x^7 +...

%e where:

%e A(x) = (1+x+x^2) * (1+x^2+x^4)^2 * (1+x^4+x^8)^4 * (1+x^8+x^16)^8 * (1+x^16+x^32)^16 *...* (1 + x^(2^n) + x^(2*2^n))^(2^n) *...

%o (PARI) {a(n)=local(A=1+x);for(i=1,#binary(n),A=(1+x+x^2)*subst(A^2,x,x^2) +x*O(x^n));polcoeff(A,n)}

%o for(n=0,50,print1(a(n),", "))

%o (PARI) {a(n)=local(A=1+x);A=prod(k=0,#binary(n),(1+x^(2^k)+x^(2*2^k)+x*O(x^n))^(2^k));polcoeff(A,n)}

%o for(n=0,50,print1(a(n),", "))

%Y Cf. A002487, A195586, A237650.

%K nonn

%O 0,3

%A _Paul D. Hanna_, May 04 2014