A110630 - OEIS

%I #7 Mar 10 2015 02:06:29

%S 1,2,3,4,1,4,3,4,3,4,2,2,4,4,3,2,2,2,3,2,3,2,4,2,2,4,2,4,2,2,1,4,1,2,

%T 4,4,1,2,3,4,4,4,3,4,2,2,2,2,1,4,1,2,3,2,4,4,1,4,1,4,2,2,3,4,2,4,2,4,

%U 3,4,4,2,4,2,1,2,4,4,4,4,1,2,4,4,2,2,3,4,1,2,2,4,1,2,4,4,3,2,3,4,1,4,4,4,3

%N Every 2nd term of A083954 such that the self-convolution 2nd power is congruent modulo 8 to A083954, which consists entirely of numbers 1 through 4.

%F a(n) = A083954(2*n) for n>=0.

%e A(x) = 1 + 2*x + 3*x^2 + 4*x^3 + x^4 + 4*x^5 + 3*x^6 + 4*x^7 +...

%e A(x)^2 = 1 + 4*x + 10*x^2 + 20*x^3 + 27*x^4 + 36*x^5 + 44*x^6 +...

%e A(x)^2 (mod 8) = 1 + 4*x + 2*x^2 + 4*x^3 + 3*x^4 + 4*x^5 +...

%e G083954(x) = 1 + 4*x + 2*x^2 + 4*x^3 + 3*x^4 + 4*x^5 + 4*x^6 +...

%e where G083954(x) is the g.f. of A083954.

%o (PARI) {a(n)=local(d=2,m=4,A=1+m*x); for(j=2,d*n, for(k=1,m,t=polcoeff((A+k*x^j+x*O(x^j))^(1/m),j); if(denominator(t)==1,A=A+k*x^j;break)));polcoeff(A,d*n)}

%Y Cf. A083954, A110629.

%K nonn

%O 0,2

%A _Robert G. Wilson v_ and _Paul D. Hanna_, Aug 09 2005