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A102877
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a(0) = 1, a(1) = 1; for n>0, a(2*n) = 3*a(2n-1), a(2*n+1) = 3*a(2*n) - 2*a(n-1).
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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
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OFFSET
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0,3
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COMMENTS
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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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LINKS
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Robert Israel, Table of n, a(n) for n = 0..2095
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FORMULA
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G.f. g(z) satisfies g(z) = 1 - 2*z + 3*z*g(z) - 2*z^3*g(z^2). - Robert Israel, Jun 29 2020
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MAPLE
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f:= proc(n) option remember; if n::even then 3*procname(n-1) else 3*procname(n-1)-2*procname((n-3)/2) fi end proc:
f(0):= 1: f(1):= 1:
map(f, [$0..50]); # Robert Israel, Jun 29 2020
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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, May 22 2007 *)
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PROG
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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.
Sequence in context: A091486 A056779 A183113 * A122983 A005355 A182399
Adjacent sequences: A102874 A102875 A102876 * A102878 A102879 A102880
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KEYWORD
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nonn
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AUTHOR
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Paul Curtz, May 16 2007
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EXTENSIONS
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More terms from Klaus Brockhaus and Stefan Steinerberger, May 20 2007
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STATUS
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approved
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