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Search: id:A103211
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| A103211 |
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(1/n) * Sum[i=0..n-1, C(n,i)*C(n,i-1)*3^i*4^(n-i) ], a(0)=1. |
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+0
13
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| 1, 4, 28, 244, 2380, 24868, 272188, 3080596, 35758828, 423373636, 5092965724, 62071299892, 764811509644, 9511373563492, 119231457692284, 1505021128450516, 19112961439180588, 244028820862442116
(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 12^C(n+1,2). - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 28 2007
The sequence 1, 1, 4, 28, .. has a(n)=0^n+sum{k=0..n-1, C(n+k-1, 2k)C(k)3^k} and Hankel transform 3^C(n+1, 2)*4^C(n, 2). [From Paul Barry (pbarry(AT)wit.ie), Dec 09 2008]
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LINKS
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E. Ackerman, G. Barequet, R. Y. Pinter and D. Romik, The number of guillotine partitions in d dimensions
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FORMULA
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G.f.: [1-z-(z^2-14z+1)^(1/2)]/(6z).
a(n)=sum{k=0..n, C(n+k, 2k)3^k*C(k)}, C(n) given by A000108. - Paul Barry (pbarry(AT)wit.ie), May 21 2005
a(n)=Sum_{k, 0<=k<=n}A060693(n,k)*3^(n-k) . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Apr 02 2007
a(0)=1, a(n)=a(n-1)+3*Sum_{k, 0<=k<=n-1}a(k)*a(n-1-k) . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 23 2007
G.f.: 1/(1-x-3x/(1-x-3x/(1-x-3x/(1-x-3x/(1-... (continued fraction). [From Paul Barry (pbarry(AT)wit.ie), Nov 07 2009]
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CROSSREFS
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Fourth column of array A103209.
Sequence in context: A093877 A151830 A112113 this_sequence A064340 A002895 A141004
Adjacent sequences: A103208 A103209 A103210 this_sequence A103212 A103213 A103214
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KEYWORD
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nonn,new
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AUTHOR
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Ralf Stephan, Jan 27 2005
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