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Search: id:A101910
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| 1, 1, 2, 2, 5, 2, 5, 5, 12, 2, 5, 5, 12, 5, 12, 12, 30, 2, 5, 5, 12, 5, 12, 12, 30, 5, 12, 12, 30, 12, 30, 30, 73, 2, 5, 5, 12, 5, 12, 12, 30, 5, 12, 12, 30, 12, 30, 30, 73, 5, 12, 12, 30, 12, 30, 30, 73, 12, 30, 30, 73, 30, 73, 73, 169, 2, 5, 5, 12, 5, 12, 12, 30, 5, 12, 12, 30, 12, 30
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OFFSET
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0,3
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COMMENT
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A101911 also forms the records in this sequence at positions 2^k for k>=0. A000120 is the binary 1's-counting sequence. Removing the even-indexed terms shifts this sequence one place left.
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FORMULA
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a(n) = Sum_{k=0, n-1} Mod(C(n-1, k), 2)*a(A000120(n-k-1)) for n>0, a(0)=1. a(2^k) = A101911(k) for k>=0.
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EXAMPLE
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Denote the n-th term of the binomial transform by: b(n)=A101911(n):
A101911 = {1,2,5,12,30,73,169,377,831,1842,4110,...}.
Note A000120 = {0,1,1,2,1,2,2,3,1,2,2,3,2,3,3,4,...}.
Then this sequence is formed by the following construct:
{1,b(0),b(1),b(1),b(2),b(1),b(2),b(2),b(3),...,b(A000120(n-1)),...}
so that a(2^0)=b(0), a(2^1)=b(1), a(2^2)=b(2), a(2^3)=b(3), ...
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PROGRAM
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(PARI) {a(n)=if(n==0, 1, sum(k=0, n-1, (binomial(n-1, k)%2)*a(subst(Pol(binary(n-k-1)), x, 1))))}
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CROSSREFS
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Cf. A101911, A000120.
Sequence in context: A128645 A007610 A068066 this_sequence A093660 A093663 A011143
Adjacent sequences: A101907 A101908 A101909 this_sequence A101911 A101912 A101913
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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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