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A156017
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Schroeder paths with two rise colors and two level colors.
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2
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1, 4, 24, 176, 1440, 12608, 115584, 1095424, 10646016, 105522176, 1062623232, 10840977408, 111811534848, 1163909087232, 12212421230592, 129027376349184, 1371482141884416, 14656212306231296, 157369985643577344
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| G.f.: (1-2x-sqrt(1-12x+4x^2))/(4x);
G.f.: 1/(1-2x-2x/(1-2x-2x/(1-2x-2x/(1-... (continued fraction);
a(n)=2^n*sum{k=0..n, C(n+k,2k)*A000108(k)}=2^n*A006318(n).
Hankel transform is 8^C(n+1,2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Feb 04 2009]
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FORMULA
| Conjecture: (n+1)*a(n) +6*(1-2*n)*a(n-1) +4*(n-2)*a(n-2)=0. - R. J. Mathar, Nov 14 2011
a(n) = Sum_{k, 0<=k<=n} A090181(n,k)*2^(n+k). - DELEHAM Philippe, Nov 27 2011
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CROSSREFS
| Sequence in context: A052685 A032349 A103334 * A000309 A112914 A007846
Adjacent sequences: A156014 A156015 A156016 * A156018 A156019 A156020
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Feb 01 2009
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EXTENSIONS
| Spelling/notation corrections by Charles R Greathouse IV (charles.greathouse(AT)case.edu), Mar 18 2010
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