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A097169
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Sum k=0..n, C(floor((n+1)/2),floor((k+1)/2))3^k.
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2
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1, 4, 13, 52, 133, 604, 1333, 6772, 13333, 74284, 133333, 801892, 1333333, 8550364, 13333333, 90286612, 133333333, 945912844, 1333333333, 9846548932, 13333333333, 101952273724, 133333333333, 1050903796852, 1333333333333
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| a(n)=(4/3){1,10,10,100,100,1000...}-9{0,1,0,9,0,81...}-(1/3){1,1,1,1,1,1...} a(2n)=A097166(n). a(2n+1)/4=A097168(n).
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (1,19,-19,-90,90)
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FORMULA
| G.f. : (1+3x-10x^2-18x^3)/((1-x)(1-9x^2)(1-10x^2)); a(n)=2((1-sqrt(10))(-sqrt(10))^n+(1+sqrt(10))(sqrt(10))^n)/3+3((-3)^n-3^n)/2-1/3; a(n)=a(n-1)+19a(n-2)-19a(n-3)-90a(n-4)+90a(n-5).
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CROSSREFS
| Cf. A097162, A075427.
Sequence in context: A135345 A149462 A151488 * A149463 A149464 A129147
Adjacent sequences: A097166 A097167 A097168 * A097170 A097171 A097172
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Jul 30 2004
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