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Search: id:A033113
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| A033113 |
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Base 3 digits are, in order, the first n terms of the periodic sequence with initial period 1,0. |
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+0
10
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| 1, 3, 10, 30, 91, 273, 820, 2460, 7381, 22143, 66430, 199290, 597871, 1793613, 5380840, 16142520, 48427561, 145282683, 435848050, 1307544150, 3922632451, 11767897353, 35303692060, 105911076180, 317733228541, 953199685623
(list; graph; listen)
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OFFSET
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1,2
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LINKS
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INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 906
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FORMULA
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E.g.f. (1/2)exp(x)(sinh(x))^2 - Paul Barry (pbarry(AT)wit.ie), Mar 12 2003
a(n)=sum{k=0..floor(n/2), C(n+2, 2k+2)4^k }. - Paul Barry (pbarry(AT)wit.ie), Aug 24 2003
a(n)=sum{k=0..floor(n/2), 3^(n-2k) }; a(n)=sum{k=0..n, sum{j=0..k, (-1)^(j+k)3^j }}. - Paul Barry (pbarry(AT)wit.ie), Nov 12 2003
Convolution of A000244 and A059841 (3^n and periodic{1, 0}). a(n)=sum{k=0..n, (1+(-1)^(n-k))3^k/2 } - Paul Barry (pbarry(AT)wit.ie), Jul 19 2004
G.f.: x/((1-x)(1+x)(1-3x)). a(n)=2a(n-1)+3a(n-2)+1. Partial sums of A015518. - Paul Barry (pbarry(AT)wit.ie), Nov 12 2003
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PROGRAM
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a(n)=if(n<0, 0, 3^n*3\8)
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CROSSREFS
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Pairwise sums seem to be in A003462.
Equals A039300 - 1.
Sequence in context: A026327 A014531 A062107 this_sequence A003441 A136841 A136846
Adjacent sequences: A033110 A033111 A033112 this_sequence A033114 A033115 A033116
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KEYWORD
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nonn
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AUTHOR
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Clark Kimberling (ck6(AT)evansville.edu)
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