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A136169
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a(n) = 2*a(n-1) - [(n+1)/3] for n>0 with a(0) = 1.
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1
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1, 2, 3, 5, 9, 16, 30, 58, 113, 223, 443, 882, 1760, 3516, 7027, 14049, 28093, 56180, 112354, 224702, 449397, 898787, 1797567, 3595126, 7190244, 14380480, 28760951, 57521893, 115043777, 230087544, 460175078, 920350146, 1840700281, 3681400551
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OFFSET
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0,2
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LINKS
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Table of n, a(n) for n=0..33.
Index entries for linear recurrences with constant coefficients, signature (3,-2,1,-3,2).
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FORMULA
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G.f.: (1 - x^2*(1+x+x^2)/(1-x^3)^2 )/(1-2*x).
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MATHEMATICA
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nxt[{n_, a_}]:={n+1, 2a-Floor[(n+2)/3]}; NestList[nxt, {0, 1}, 50][[All, 2]] (* Harvey P. Dale, Aug 09 2021 *)
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PROG
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(PARI) {a(n)=if(n==0, 1, 2*a(n-1)-((n+1)\3))}
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CROSSREFS
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Cf. A136219.
Sequence in context: A329700 A217282 A047061 * A047041 A352944 A154223
Adjacent sequences: A136166 A136167 A136168 * A136170 A136171 A136172
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KEYWORD
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nonn,easy
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AUTHOR
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Paul D. Hanna, Dec 23 2007
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STATUS
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approved
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