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Search: id:A033114
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| A033114 |
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Base-4 digits are, in order, the first n terms of the periodic sequence with initial period 1,0. |
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+0
4
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| 1, 4, 17, 68, 273, 1092, 4369, 17476, 69905, 279620, 1118481, 4473924, 17895697, 71582788, 286331153, 1145324612, 4581298449, 18325193796, 73300775185, 293203100740, 1172812402961, 4691249611844, 18764998447377, 75059993789508
(list; graph; listen)
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OFFSET
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1,2
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FORMULA
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a(n) = floor(4^(n+1)/15) = 4^(n+1)/15-1/6-(-1)^n/10. - Benoit Cloitre (benoit7848c(AT)orange.fr), Apr 18 2003
a(n)=sum{k=0..floor(n/2), 4^(n-2k) }; a(n)=sum{k=0..n, sum{j=0..k, (-1)^(j+k)4^j }}. - Paul Barry (pbarry(AT)wit.ie), Nov 12 2003
G.f.: 1/((1-x)(1+x)(1-4x)); a(n)=3a(n-1)+4a(n-2)+1. Partial sum of A015521. - Paul Barry (pbarry(AT)wit.ie), Nov 12 2003
Convolution of A000302 and A059841 (4^n and periodic{1, 0}). a(n)=sum{k=0..n, (1+(-1)^(n-k))4^k/2 } - Paul Barry (pbarry(AT)wit.ie), Jul 19 2004
a(n)=sum{k=0..n, (-1)^(n-k)*(J(2k+1)-1)/2}, J(n)=A001045(n); - Paul Barry (pbarry(AT)wit.ie), Mar 06 2008
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CROSSREFS
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Sequence in context: A030529 A081113 A114587 this_sequence A096881 A033122 A005511
Adjacent sequences: A033111 A033112 A033113 this_sequence A033115 A033116 A033117
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KEYWORD
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nonn,base
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AUTHOR
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Clark Kimberling (ck6(AT)evansville.edu)
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