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Search: id:A108981
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| A108981 |
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a(n) = 3a(n-1) + 4a(n-2), a(0) = 1, a(1) = 5.. |
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+0
4
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| 1, 5, 19, 77, 307, 1229, 4915, 19661, 78643, 314573, 1258291, 5033165, 20132659, 80530637, 322122547, 1288490189, 5153960755, 20615843021, 82463372083, 329853488333, 1319413953331, 5277655813325, 21110623253299
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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The Hankel transform of this sequence is [1,-6,0,0,0,0,0,0,0,0,...]. - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Apr 15 2008
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FORMULA
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Inverse binomial transform of A003948.
a(2n) = 4a(2n-1) - 1; a(2n+1) = 4a(2n) + 1.
a(n) = 3*2^(2*n-1)-a(n-1), with a(0) = 1; also a(n) = abs{3*sum[i = 1..n,(-1)^i*2^(2*i-1)]+1}, with a(0) = 1. - Paolo P. Lava & Giorgio Balzarotti (ppl(AT)spl.at), May 28 2007
O.g.f.: -(1+2*x)/[(1+x)(4*x-1)]. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 02 2008
Sum_{k, 0<=k<=n}a(k)=A037481(n+1). - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Apr 15 2008
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MAPLE
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P:=proc(n, k) local a, i, j; a:=1; print(a); for i from 1 by 1 to n do j:=(k+1)*k^(2*i-1)-a; print(j); a:=j; od; end: P(100, 2); - Paolo P. Lava & Giorgio Balzarotti (ppl(AT)spl.at), May 28 2007
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CROSSREFS
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Sequence in context: A149768 A149769 A149770 this_sequence A149771 A149772 A149773
Adjacent sequences: A108978 A108979 A108980 this_sequence A108982 A108983 A108984
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KEYWORD
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nonn
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AUTHOR
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Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Jul 23 2005
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EXTENSIONS
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Corrected by T. D. Noe (noe(AT)sspectra.com), Nov 07 2006
Edited by N. J. A. Sloane (njas(AT)research.att.com) at the suggestion of R. J. Mathar, Apr 14 2008
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