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Search: id:A108073
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| 1, 1, 1, 3, 2, 1, 9, 7, 3, 1, 31, 24, 12, 4, 1, 113, 89, 46, 18, 5, 1, 431, 342, 183, 76, 25, 6, 1, 1697, 1355, 741, 323, 115, 33, 7, 1, 6847, 5492, 3054, 1376, 520, 164, 42, 8, 1, 28161, 22669, 12768, 5900, 2326, 786, 224, 52, 9, 1, 117631, 94962, 54033, 25464
(list; table; graph; listen)
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OFFSET
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0,4
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COMMENT
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A convolution triangle based on A052709 (with first term omitted). - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Sep 15 2005
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FORMULA
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G.f.=(1-q)/[z(2-t+2z+tq)], where q=sqrt(1-4z-4z^2). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Jun 06 2005
T(0, 0) = 1; T(n, k) = 0 if k<0 or if k>n; T(n, k) = Sum_{j, j>=0} T(n-1, k-1+j) + Sum_{j, j>=0} T(n-1, k+1+j) . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Sep 15 2005
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EXAMPLE
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1; 1,1; 3,2,1; 9,7,3,1; 31,24,12,4,1; ...
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MAPLE
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q:=sqrt(1-4*z-4*z^2): G:=(1-q)/z/(2-t+2*z+t*q): Gserz:=simplify(series(G, z=0, 14)): P[0]:=1: for n from 1 to 10 do P[n]:=coeff(Gserz, z^n) od: for n from 0 to 10 do seq(coeff(t*P[n], t^k), k=1..n+1) od; # yields sequence in triangular form (Deutsch)
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CROSSREFS
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Row sums yield A071356. Column 0 yields A052709.
Sequence in context: A002350 A109267 A155788 this_sequence A057731 A126074 A108916
Adjacent sequences: A108070 A108071 A108072 this_sequence A108074 A108075 A108076
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KEYWORD
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nonn,tabl,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Jun 05 2005
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EXTENSIONS
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More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Jun 06 2005
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