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Search: id:A135364
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| A135364 |
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First column of a triangle - see Comments lines. |
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+0
3
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| 1, 2, 3, 7, 17, 40, 93, 216, 502, 1167, 2713, 6307, 14662, 34085, 79238, 184206, 428227, 995507, 2314273, 5380032, 12507057, 29075380, 67592058, 157132471, 365288677, 849193147, 1974134558, 4589306057, 10668842202
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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...1;
...2,...1;
...3,...3,...1;
...7,...5,...4,...1;
..17,..10,...7,...5,...1;
..40,..24,..13,...9,...6,...1;
..93,..57,..31,..16,..11,...7,...1;
From the second, the sum of a row gives the first term of the following one.Diagonal differences are the first term upon. First column is a(n).
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FORMULA
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a(n+1) = a(n)+a(n-1)+(n-1)*a(1)+(n-2)*a(2)+...+2*a(n-2) for n>=3. O.g.f : h such that h(z)=a(1)*z+a(2)*z^2+...=((z-z^2-z^3+z^4)/(1-3*z+2*z^2-z^3)). Also a(n+3) = 3*a(n+2)-2*a(n+1)+a(n). - Richard Choulet (richardchoulet(AT)yahoo.fr), Jan 06 2008
a(n)=A034943(n)+A034943(n+1). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 09 2008
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CROSSREFS
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Cf. A097550 whose o.g.f is given by (1+z^2)/(1-3*z+2*z^2-z^3).
Sequence in context: A078721 A077007 A105554 this_sequence A051291 A113483 A059801
Adjacent sequences: A135361 A135362 A135363 this_sequence A135365 A135366 A135367
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KEYWORD
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nonn
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AUTHOR
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Paul Curtz (bpcrtz(AT)free.fr), Dec 09 2007
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EXTENSIONS
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More terms from Richard Choulet (richardchoulet(AT)yahoo.fr), Jan 06 2008
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