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Every 2-nd term of A083946 where the self-convolution 2-nd power is congruent modulo 4 to A083946, which consists entirely of numbers 1 through 6.

+0
3

1, 3, 3, 6, 3, 6, 6, 3, 6, 3, 6, 3, 6, 3, 6, 2, 6, 6, 6, 3, 6, 4, 6, 6, 4, 3, 3, 6, 3, 3, 3, 3, 6, 2, 3, 3, 1, 6, 6, 2, 6, 6, 3, 3, 6, 1, 6, 6, 6, 3, 6, 6, 3, 6, 1, 6, 6, 2, 3, 6, 6, 3, 3, 4, 6, 6, 2, 3, 6, 4, 3, 6, 2, 6, 3, 6, 3, 6, 2, 6, 6, 4, 3, 3, 2, 3, 3, 6, 3, 3, 5, 3, 3, 2, 6, 6, 2, 3, 6, 1, 3, 3, 5, 3, 6 (list; graph; listen)

	OFFSET	`0,2`
	EXAMPLE	`A(x) = 1 + 3x + 3x^2 + 6x^3 + 3x^4 + 6x^5 + 6x^6 +...` `A(x)^2 = 1 + 6x + 15x^2 + 30x^3 + 51x^4 + 66x^5 +...` `A(x)^2 (mod 4) = 1 + 2x + 3x^2 + 2x^3 + 3x^4 + 2x^5 +...` `G(x) = 1 + 6x + 3x^2 + 2x^3 + 3x^4 + 6*x^5 +...` `where G(x) is the g.f. of A083946.`
	PROGRAM	`(PARI) {a(n)=local(d=2, m=6, A=1+mx); for(j=2, dn, for(k=1, m, t=polcoeff((A+kx^j+xO(x^j))^(1/m), j); if(denominator(t)==1, A=A+kx^j; break))); polcoeff(A, dn)}`
	CROSSREFS	`Cf. A110632, A110633.` `Sequence in context: A020813 A034188 A040007 this_sequence A151787 A113397 A007425` `Adjacent sequences: A110631 A110632 A110633 this_sequence A110635 A110636 A110637`
	KEYWORD	`nonn`
	AUTHOR	`Robert G. Wilson v (rgwv(AT)rgwv.com) and Paul D. Hanna (pauldhanna(AT)juno.com), Aug 30 2005`

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Last modified November 25 20:09 EST 2009. Contains 167514 sequences.

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