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A223142 G.f. satisfies: A(x)^2 = A(x^2)^2 + 4*x. 2

%I #5 Mar 15 2013 11:57:43

%S 1,2,0,0,2,-4,8,-16,32,-56,88,-112,64,240,-1264,4064,-10814,25500,

%T -54200,102832,-166020,190808,22304,-1058880,4412424,-13496544,

%U 35306480,-82326496,172081840,-315115328,464910368,-363016000,-871587808,5713552456,-20289991016

%N G.f. satisfies: A(x)^2 = A(x^2)^2 + 4*x.

%H Paul D. Hanna, <a href="/A223142/b223142.txt">Table of n, a(n) for n = 0..500</a>

%F G.f.: A(x) = sqrt( 1 + Sum_{n>=0} 4*x^(2^n) ).

%e G.f.: A(x) = 1 + 2*x + 2*x^4 - 4*x^5 + 8*x^6 - 16*x^7 + 32*x^8 - 56*x^9 +...

%e where

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

%o (PARI) {a(n)=local(A=1+x); for(i=1,#binary(n), A=(subst(A, x, x^2)^2+4*x+x*O(x^n))^(1/2)); polcoeff(A, n, x)}

%o for(n=0,40,print1(a(n),", "))

%Y Cf. A223143, A107086, A223026.

%K sign

%O 0,2

%A _Paul D. Hanna_, Mar 15 2013

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Last modified February 26 17:57 EST 2024. Contains 370352 sequences. (Running on oeis4.)