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A064630
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Number of parts if 4^n is partitioned into parts of size 3^n as far as possible into parts of size 2^n as far as possible and into parts of size 1^n.
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5
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2, 5, 5, 16, 25, 15, 66, 121, 146, 771, 1220, 3641, 8093, 15843, 28359, 50236, 33366, 36709, 145250, 137776, 548024, 2186496, 1066102, 4251976, 16984368, 28678103, 13620614, 205950171, 100716646, 381399635, 1397934923, 3826001641
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OFFSET
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1,1
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COMMENTS
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Corresponds to the only solution of the Diophantine equation 4^n = x*3^n + y*2^n + z*1^n with constraints 0 <= y < 3^n/2^n, 0 <= z < 2^n.
Binary order (cf. A029837) of a(n) is close to n.
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LINKS
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Harry J. Smith, Table of n, a(n) for n=1,...,250
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FORMULA
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a(n) = A064628(n) + floor(A064629(n)/2^n) + (A064629(n) mod 2^n) = floor(4^n/3^n) + floor((4^n mod 3^n)/2^n) + ((4^n mod 3^n) mod 2^n)
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EXAMPLE
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4^6 = 4096 = 729 + 729 + 729 + 729 + 729 + 64 + 64 + 64 + 64 + 64 + 64 + 64 + 1 + 1 + 1 = 5*3^6 + 7*2^6 + 3*1^6, so a(6) = 5 + 7 + 3 = 15.
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PROG
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(PARI) {for(n=1, 32, a=divrem(4^n, 3^n); b=divrem(a[2], 2^n); print1(a[1]+b[1]+b[2], ", "))}
(PARI) { f=t=w=1; for (n=1, 250, f*=4; t*=3; w*=2; a=divrem(f, t); b=divrem(a[2], w); write("b064630.txt", n, " ", a[1]+b[1]+b[2]) ) } [From Harry J. Smith, Sep 20 2009]
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CROSSREFS
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Cf. A064628, A064629, A060692, A029837.
Sequence in context: A121304 A002106 A184604 * A089793 A076570 A089121
Adjacent sequences: A064627 A064628 A064629 * A064631 A064632 A064633
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KEYWORD
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nonn
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu), Oct 01 2001
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EXTENSIONS
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Edited by Klaus Brockhaus, May 24 2003
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STATUS
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approved
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