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Search: id:A060925
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| A060925 |
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a(n) = 2a(n-1) + 3a(n-2), a(0) = 1, a(1) = 4. |
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+0
7
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| 1, 4, 11, 34, 101, 304, 911, 2734, 8201, 24604, 73811, 221434, 664301, 1992904, 5978711, 17936134, 53808401, 161425204, 484275611, 1452826834, 4358480501, 13075441504, 39226324511, 117678973534, 353036920601
(list; graph; listen)
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OFFSET
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0,2
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FORMULA
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Row sums of Lucas convolution triangle A060922.
Inverse binomial transform of A003947. - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Jul 23 2005
a(n)=sum(A060922(n, m), m=0..n) = sum(a(j-1)*A000204(n-j+1), j=1..n)+A000204(n+1).
a(n)=(5*3^n-(-1)^n)/4.
G.f.: (1+2*x)/(1-2*x-3*x^2).
a(2n) = 3a(2n-1) - 1; a(2n+1) = 3a(2n) + 1. - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Jul 23 2005
Binomial transform is A003947. - Paul Barry (pbarry(AT)wit.ie), May 19 2003
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CROSSREFS
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Sequence in context: A127154 A062460 A098324 this_sequence A027045 A006765 A112272
Adjacent sequences: A060922 A060923 A060924 this_sequence A060926 A060927 A060928
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KEYWORD
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nonn,easy
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Apr 20 2001
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EXTENSIONS
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Recurrence, now used as definition, from Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Jul 23 2005
Entry revised by njas, Sep 10 2006
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