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Search: id:A070998
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| A070998 |
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a(n) = 9*a(n-1) - a(n-2), a(0)=1, a(-1)=1. |
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+0
5
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| 1, 8, 71, 631, 5608, 49841, 442961, 3936808, 34988311, 310957991, 2763633608, 24561744481, 218292066721, 1940066856008, 17242309637351, 153240719880151, 1361924169284008, 12104076803675921
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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A Pellian sequence.
In general, sum{k=0..n, binomial(2n-k,k)j^(n-k)}=(-1)^n*U(2n,I*sqrt(j)/2), I=sqrt(-1); - Paul Barry (pbarry(AT)wit.ie), Mar 13 2005
a(n) = L(n,9), where L is defined as in A108299; see also A057081 for L(n,-9). - Reinhard Zumkeller (reinhard.zumkeller(AT)lhsystems.com), Jun 01 2005
Number of 01-avoiding words of length n on alphabet {0,1,2,3,4,5,6,7,8} which do not end in 0. - Tanya Khovanova (tanyakh(AT)yahoo.com), Jan 10 2007
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LINKS
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Tanya Khovanova, Recursive Sequences
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FORMULA
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a(n) ~ 1/11*sqrt(11)*(1/2*(sqrt(11)+sqrt(7)))^(2*n+1)
Let q(n, x)=sum(i=0, n, x^(n-i)*binomial(2*n-i, i)); then q(n, 7)=a(n) - Benoit Cloitre (benoit7848c(AT)orange.fr), Nov 10 2002
a(n)a(n+3) = 63 + a(n+1)a(n+2). - R. Stephan, May 29 2004
a(n)=(-1)^n*U(2n, I*sqrt(7)/2), U(n, x) Chebyshev polynomial of second kind, I=sqrt(-1); - Paul Barry (pbarry(AT)wit.ie), Mar 13 2005
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CROSSREFS
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Cf. A057081, A056918.
Row 9 of array A094954.
Adjacent sequences: A070995 A070996 A070997 this_sequence A070999 A071000 A071001
Sequence in context: A003364 A038145 A015576 this_sequence A081178 A096341 A075506
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KEYWORD
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nonn
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AUTHOR
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Joe Keane (jgk(AT)jgk.org), May 18 2002
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