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Search: id:A158524
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| A158524 |
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Choulet-Curtz triangle with T(0,0)=1, T(n,n)=T(n,0). |
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1
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| 1, 1, 1, 2, 2, 2, 6, 3, 3, 6, 18, 4, 4, 8, 18, 52, 5, 5, 10, 24, 52, 148, 6, 6, 12, 30, 70, 148, 420, 7, 7, 14, 36, 88, 200, 420, 1192, 8, 8, 16, 42, 106, 252, 568, 1192, 3384, 9, 9, 18, 48, 124, 304, 716, 1612, 3384, 9608, 10, 10, 20, 54, 142, 356, 864, 2032, 4576, 9608
(list; table; graph; listen)
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OFFSET
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0,4
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COMMENT
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Row sums are in A078484 .
This sequence is an example of a sequence u(n) which satisfies (using the notation of http://apmep.asso.fr/IMG/pdf/curtz1/pdf): T_{1,1}(u(0), u(1), u(2), u(3), ...)=(u(1), u(2), u(3), ...). The O.g.f of all such sequences is given by the formula : Phi(z)=u(0)*((1-3*z+2*z^2-z^3)/(1-4*z+4*z^2-2*z^3))+((z+z^3)/(1-4*z+4*z^2-2*z^3)) with u(0) in N or Z ; the sequences are given by : u(n)=u(0)*(1, 1, 2, 5, 14, 40, 114, 324, 920, ...)+(0, 1, 4, 13, 38, 108, 868, 2464, 6996, ...) i.e. u(n)=u(0)*A159035(n)+A159036(n). [From Richard Choulet (richardchoulet(AT)yahoo.fr), Apr 03 2009]
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FORMULA
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T(n,k)=T(n-1,k)+T(k-1,k-1), k>=1, n>k ; T(n,n)=T(n,0)=Sum_{k, 0<=k<=n}T(n-1,k) ; T(0,0)=1 .
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EXAMPLE
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Triangle begins : 1 ; 1, 1 ; 2, 2, 2 ; 6, 3, 3, 6 ; 18, 4, 4, 8, 18 ; 52, 5, 5, 10, 24, 52 ; 148, 6, 6, 12, 30, 70, 148 ;
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CROSSREFS
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Cf. A078484
Cf. A159035, A159036 [From Richard Choulet (richardchoulet(AT)yahoo.fr), Apr 03 2009]
Sequence in context: A097521 A081668 A126615 this_sequence A054274 A053695 A119918
Adjacent sequences: A158521 A158522 A158523 this_sequence A158525 A158526 A158527
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KEYWORD
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nonn,tabl
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AUTHOR
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Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Mar 20 2009
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