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A078932
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Number of ordered partitions of n into powers of 3.
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4
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1, 1, 1, 2, 3, 4, 6, 9, 13, 20, 30, 44, 66, 99, 147, 219, 327, 487, 726, 1083, 1614, 2406, 3588, 5349, 7974, 11889, 17725, 26426, 39399, 58739, 87573, 130563, 194655, 290208, 432669, 645062, 961716, 1433814, 2137659, 3187014, 4751490, 7083951
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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LINKS
| T. D. Noe, Table of n, a(n) for n=0..500
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FORMULA
| G.f. satisfies A(x) = A(x^3)/(1 - x*A(x^3)), A(0) = 1.
Sum(k>=0, a(2k+1)*x^k) / sum(k>=0, a(2k)*x^k) = sum(k>=0, x^((3^n-1)/2)) = (1 +2x +4x^2 +9x^3 +20x^4 +...)/(1 +x +3x^2 +6x^3 +13x^4 +...) = (1 +x +x^4 +x^13 +x^40 +x^121 +...).
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EXAMPLE
| A(x) = A(x^3) + x*A(x^3)^2 + x^2*A(x^3)^3 + x^3*A(x^3)^4 + ... = 1 +x + x^2 +2x^3 +3x^4 +4x^5 +6x^6 +9x^7 + 13x^8 +...
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PROG
| (PARI) a(n)=local(A, m); if(n<1, n==0, m=1; A=1+O(x); while(m<=n, m*=3; A=1/(1/subst(A, x, x^3)-x)); polcoeff(A, n))
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CROSSREFS
| Cf. A023359.
Cf. A087218, A087219.
Sequence in context: A121653 A061418 A136423 * A206740 A172161 A117791
Adjacent sequences: A078929 A078930 A078931 * A078933 A078934 A078935
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KEYWORD
| nonn
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Dec 16 2002
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EXTENSIONS
| New description from T. D. Noe, Jan 29 2007
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