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Search: id:A101911
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| 1, 2, 5, 12, 30, 73, 169, 377, 831, 1842, 4110, 9136, 20006, 42906, 90148, 186414, 381955, 780966, 1603330, 3319952, 6949554, 14704880, 31379910, 67272276, 144212735, 307752571, 651353609, 1363714711, 2820488954, 5761343912
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OFFSET
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0,2
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COMMENT
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Also gives the records in A101910 at positions 2^n for n>=0. A000120 is the binary 1's-counting sequence.
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FORMULA
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a(n) = 1 + Sum_{k=0, n-1} C(n, k)*a(A000120(n-k-1)) for n>0, a(0)=1. a(n) = A101910(2^n) for n>=0.
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EXAMPLE
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Equals the binomial transform of A101910, where
A101910 = {1,1,2,2,5,2,5,5,12,2,5,5,12,5,12,12,30,...}
which has the following construction:
{1,a(0),a(1),a(1),a(2),a(1),a(2),a(2),a(3),...,a(A000120(n-1)),...}
where A000120 = {0,1,1,2,1,2,2,3,1,2,2,3,2,3,3,4,...}.
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PROGRAM
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(PARI) {a(n)=if(n==0, 1, 1+sum(k=0, n-1, binomial(n, k)*a(subst(Pol(binary(n-k-1)), x, 1))))}
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CROSSREFS
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Cf. A101910, A000120.
Sequence in context: A132807 A101411 A042789 this_sequence A052109 A046170 A062423
Adjacent sequences: A101908 A101909 A101910 this_sequence A101912 A101913 A101914
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KEYWORD
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eigen,nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Dec 21 2004
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