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Search: id:A102877
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| A102877 |
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a(0) = 1, a(1) = 1; for n>0, a(2n) = 3a(2n-1), a(2n+1) = 3a(2n) - 2a(n-1). |
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+0
2
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| 1, 1, 3, 7, 21, 61, 183, 543, 1629, 4873, 14619, 43815, 131445, 394213, 1182639, 3547551, 10642653, 31926873, 95780619, 287338599, 862015797, 2586037645, 7758112935, 23274309567, 69822928701, 209468698473, 628406095419
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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The sequence of first differences of these numbers (2, 4, 14, 40 ...), divided by 2, is (1, 2, 7, 20, ...) - see A111017. This is close to the original sequence.
..... 1, 1, 3, 7, 21, 61, 183, 543, 1629, 4873, 14619
........ 1, 2, 7, 20, 61, 180, 543, 1622, 4873, 14598
....... 2=3-1, 20=21-1, 180=183-3, 1622=1629-7, 14598=14619-21
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MATHEMATICA
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a[0]:=1; a[1]:=1; a[n_]:=If[EvenQ[n], 3*a[n-1], 3*a[n-1]-2*a[(n-3)/2]]; Table[a[i], {i, 0, 50}] - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), May 22 2007
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PROGRAM
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(PARI) {m=26; v=vector(m+1); v[1]=1; v[2]=1; for(n=2, m, k=3*v[n]; if(n%2==1, k=k-2*v[(n-1)/2]); v[n+1]=k); print(v)} /* Klaus Brockhaus, May 20 2007 */
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CROSSREFS
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This sequence is connected with A129770 and A129772.
Adjacent sequences: A102874 A102875 A102876 this_sequence A102878 A102879 A102880
Sequence in context: A035080 A091486 A056779 this_sequence A122983 A005355 A025235
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KEYWORD
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nonn
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AUTHOR
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Paul Curtz (bpcrtz(AT)free.fr), May 16 2007
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EXTENSIONS
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More terms from Klaus Brockhaus (klaus-brockhaus(AT)t-online.de) and Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), May 20 2007
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