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A103321
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Expansion of 1 / [(1-x-x^2-x^3)(1-x-x^3)].
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0
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1, 2, 4, 9, 18, 35, 68, 130, 246, 463, 867, 1617, 3007, 5579, 10332, 19107, 35295, 65140, 120137, 221444, 407999, 751453, 1383641, 2547116, 4688106, 8627504, 15875390, 29209560, 53739655, 98864470, 181872110, 334561861, 615423932
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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REFERENCES
| A. T. Benjamin and J. J. Quinn, Proofs that really count: the art of combinatorial proof, M.A.A. 2003, p. 47, ex. 4.
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FORMULA
| a(n) = A000073(n+4) - A000930(n+2) = Sum[k=0..n, A000073(k+2)*A000930(n-k) ].
a(0)=1, a(1)=2, a(2)=4, a(3)=9, a(4)=18, a(5)=35, a(n)=2*a(n-1)+a(n-3)- 2*a(n-4)-a(n-5)-a(n-6) [From Harvey P. Dale, Nov 06 2011]
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MATHEMATICA
| CoefficientList[Series[1/((1-x-x^2-x^3)(1-x-x^3)), {x, 0, 40}], x] (* or *) LinearRecurrence[{2, 0, 1, -2, -1, -1}, {1, 2, 4, 9, 18, 35}, 40] (* From Harvey P. Dale, Nov 06 2011 *)
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CROSSREFS
| Sequence in context: A046683 A065055 A065030 * A138196 A101351 A111662
Adjacent sequences: A103318 A103319 A103320 * A103322 A103323 A103324
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KEYWORD
| nonn
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AUTHOR
| Ralf Stephan, Feb 02 2005
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