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A087221
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Number of ordered partitions of n into powers of 4.
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4
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1, 1, 1, 1, 2, 3, 4, 5, 7, 10, 14, 19, 26, 36, 50, 69, 96, 133, 184, 254, 352, 488, 676, 935, 1294, 1792, 2482, 3436, 4756, 6584, 9116, 12621, 17473, 24190, 33490, 46365, 64190, 88868, 123034, 170334, 235818, 326478, 451994, 625764, 866338, 1199400, 1660510
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| sum(k>=0,a(3k+1)*x^k) / sum(k>=0,a(3k)*x^k) = sum(k>=0,a(3k+2)*x^k) / sum(k>=0,a(3k+1)*x^k) = sum(k>=0,a(3k+3)*x^k) / sum(k>=0,a(3k+2)*x^k) = sum(k>=0,x^((4^n-1)/3)) = (1 +x +x^5 +x^21 +x^85 +x^341 +...).
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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^4)/(1 - x*A(x^4)), A(0) = 1.
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EXAMPLE
| A(x) = A(x^4) + x*A(x^4)^2 + x^2*A(x^4)^3 + x^3*A(x^4)^4 + ...
= 1 +x + x^2 +x^3 +2x^4 +3x^5 +5x^6 +7x^7 + 10x^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*=4; A=1/(1/subst(A, x, x^4)-x)); polcoeff(A, n))
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CROSSREFS
| Cf. A078932, A087222, A087232, A087224. Different from A003269.
Sequence in context: A099559 A017898 A003269 * A206739 A107586 A206737
Adjacent sequences: A087218 A087219 A087220 * A087222 A087223 A087224
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KEYWORD
| nonn
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Aug 27 2003
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