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A138635
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a(n) =3*a(n-3)-3*a(n-6)+2*a(n-9).
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3
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0, 0, 1, 0, 1, 1, 1, 2, 1, 3, 3, 2, 6, 5, 5, 11, 10, 11, 21, 21, 22, 42, 43, 43, 85, 86, 85, 171, 171, 170, 342, 341, 341, 683, 682, 683, 1365, 1365, 1366, 2730, 2731, 2731, 5461, 5462, 5461, 10923, 10923, 10922, 21846, 21845, 21845, 43691, 43690, 43691, 87381
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,8
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COMMENTS
| As the recurrence shows, these are three interleaved sequences which obey recurrences b(n)=3*b(n-1)-3*b(n-2)+2*b(n-3),
indicating that the b(n) equal their third differences.
These three sequences are A024495, A024494 (or A131708) and A024493 (or A130781).
Their starting "vectors" b(0,1,2) are 0,0,1 and 0,1,2 and 1,1,1, respectively, therefore linearly independent, such that
other sequences with the same recursion as b(n) can be written as linear combinations of these.
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LINKS
| Index entries for sequences related to linear recurrences with constant coefficients
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FORMULA
| a(18n)= 21*A133853(n).
G.f.: -x^2*(1+x^2-2*x^3+x^4-x^5+x^6)/((2*x^3-1)*(x^6-x^3+1)). [R. J. matMathar, May 17 2009]
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CROSSREFS
| Sequence in context: A133341 A111492 A144305 * A128182 A059739 A035566
Adjacent sequences: A138632 A138633 A138634 * A138636 A138637 A138638
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KEYWORD
| nonn,easy
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AUTHOR
| Paul Curtz (bpcrtz(AT)free.fr), May 14 2008
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EXTENSIONS
| Edited by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 17 2009
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