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Search: id:A110630
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| A110630 |
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Every 2-nd term of A083954 such that the self-convolution 2-nd power is congruent modulo 8 to A083954, which consists entirely of numbers 1 through 4. |
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3
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| 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, 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, 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
(list; graph; listen)
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OFFSET
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0,2
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FORMULA
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a(n) = A083954(2*n) for n>=0.
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EXAMPLE
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A(x) = 1 + 2*x + 3*x^2 + 4*x^3 + x^4 + 4*x^5 + 3*x^6 + 4*x^7 +...
A(x)^2 = 1 + 4*x + 10*x^2 + 20*x^3 + 27*x^4 + 36*x^5 + 44*x^6 +...
A(x)^2 (mod 8) = 1 + 4*x + 2*x^2 + 4*x^3 + 3*x^4 + 4*x^5 +...
G083954(x) = 1 + 4*x + 2*x^2 + 4*x^3 + 3*x^4 + 4*x^5 + 4*x^6 +...
where G083954(x) is the g.f. of A083954.
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PROGRAM
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(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)}
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CROSSREFS
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Cf. A083954, A110629.
Sequence in context: A138223 A159798 A003324 this_sequence A129717 A117742 A117716
Adjacent sequences: A110627 A110628 A110629 this_sequence A110631 A110632 A110633
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KEYWORD
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nonn
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AUTHOR
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Robert G. Wilson v (rgwv(AT)rgwv.com) and Paul D. Hanna (pauldhanna(AT)juno.com), Aug 09 2005
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