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A135364
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First column of a triangle - see Comments lines.
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5
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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; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| ...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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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (3,-2,1).
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FORMULA
| 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 1 -x*(2-3*x+2*x^2) / ( -1+3*x-2*x^2+x^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
a(0) = 1, a(n) = term (1,3) in the 1x3 matrix [7,3,2].[3,1,0; -2,0,1; 1,0,0]^(n-1) (n>0). - Alois P. Heinz (heinz(AT)hs-heilbronn.de), Jul 24 2008
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MAPLE
| a := n -> if n=0 then 1 else (Matrix([[7, 3, 2]]) . Matrix([[3, 1, 0], [ -2, 0, 1], [1, 0, 0]])^(n-1))[1, 3] fi; seq (a(n), n=0..50); - Alois P. Heinz (heinz(AT)hs-heilbronn.de), Jul 24 2008
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MATHEMATICA
| Join[{1, 2}, a=0; b=1; c=2; Table[a+=b; b+=c; c+=a, {n, 50}]] [From Vladimir Joseph Stephan Orlovsky (4vladimir(AT)gmail.com), Nov 19 2010]
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CROSSREFS
| Cf. A097550.
Sequence in context: A191033 A105554 A145230 * A051291 A178178 A143013
Adjacent sequences: A135361 A135362 A135363 * A135365 A135366 A135367
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KEYWORD
| nonn
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AUTHOR
| Paul Curtz (bpcrtz(AT)free.fr), Dec 09 2007
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EXTENSIONS
| More terms from Richard Choulet (richardchoulet(AT)yahoo.fr), Jan 06 2008
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