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Search: id:A161809
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| A161809 |
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G.f.: A(x) = exp( Sum_{n>=1} 3*A038500(n) * x^n/n ), where A038500 is the highest power of 3 dividing n. |
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2
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| 1, 3, 6, 12, 21, 33, 51, 75, 105, 147, 201, 267, 354, 462, 591, 753, 948, 1176, 1455, 1785, 2166, 2622, 3153, 3759, 4470, 5286, 6207, 7275, 8490, 9852, 11415, 13179, 15144, 17376, 19875, 22641, 25761, 29235, 33063, 37353, 42105, 47319, 53124
(list; graph; listen)
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OFFSET
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0,2
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FORMULA
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Contribution from Paul D. Hanna (pauldhanna(AT)juno.com), Jul 27 2009: (Start)
G.f. satisfies: A(x) = A(x^3)*(1+x+x^2)/(1-x)^2.
Define TRISECTIONS: A(x) = T_0(x^3) + x*T_1(x^3) + x^2*T_2(x^3), then:
T_1(x)/T_0(x) = 3*(1 + 2*x)/(1 + 7*x + x^2) and
T_2(x)/T_0(x) = 3*(2 + x)/(1 + 7*x + x^2).
(End)
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EXAMPLE
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G.f.: A(x) = 1 + 3*x + 6*x^2 + 12*x^3 + 21*x^4 + 33*x^5 + 51*x^6 +...
log(A(x)) = 3*x + 3*x^2/2 + 9*x^3/3 + 3*x^4/4 + 3*x^5/5 + 9*x^6/6 +...
Contribution from Paul D. Hanna (pauldhanna(AT)juno.com), Jul 27 2009: (Start)
TRISECTIONS begin:
T_0(x) = 1 + 12*x + 51*x^2 + 147*x^3 + 354*x^4 + 753*x^5 +...
T_1(x) = 3 + 21*x + 75*x^2 + 201*x^3 + 462*x^4 + 948*x^5 +...
T_2(x) = 6 + 33*x + 105*x^2 + 267*x^3 + 591*x^4 + 1176*x^5 +...
(End)
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PROGRAM
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(PARI) {a(n)=local(L=sum(m=1, n, 3*3^valuation(m, 3)*x^m/m)+x*O(x^n)); polcoeff(exp(L), n)}
(PARI) {a(n)=local(A=1+x); for(i=0, n\3, A=subst(A, x, x^3+x*O(x^n))*(1+x+x^2)/(1-x+x*O(x^n))^2); polcoeff(A, n)} [From Paul D. Hanna (pauldhanna(AT)juno.com), Jul 27 2009]
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CROSSREFS
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Cf. A000123.
Sequence in context: A053479 A070333 A011779 this_sequence A084439 A034344 A054578
Adjacent sequences: A161806 A161807 A161808 this_sequence A161810 A161811 A161812
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Jul 20 2009
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