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A142965
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One fourth of third column (m=2) of triangle A142963.
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6
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1, 18, 129, 646, 2685, 10002, 34777, 115566, 372453, 1175290, 3654369, 11245110, 34349005, 104373282, 315969705, 954002878, 2874983541, 8652474378, 26015617585, 78169534470, 234766551261, 704840716978, 2115654610809, 6349329417486, 19052920751365, 57169029907482
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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FORMULA
| a(n)= A142693(n+3,2)/4.
Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), Feb 20 2009: (Start)
a(n) = 10a(n-1)-40a(n-2)+82a(n-3)-91a(n-4)+52a(n-5)-12a(n-6)
a(n) = 35/2+2*n^2+12*n-84*2^n-24*2^n*n+135/2*3^n
G.f.: (1+8*z-11*z^2-6*z^3)/((1-z)^3*(1-2*z)^2*(1-3*z))
(End)
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MATHEMATICA
| LinearRecurrence[{10, -40, 82, -91, 52, -12}, {1, 18, 129, 646, 2685, 10002}, 30] (* or *) CoefficientList[Series[(1+8x-11x^2-6x^3)/((x-1)^3 (2x-1)^2 (3x-1)), {x, 0, 30}], x] (* From Harvey P. Dale, Apr 24 2011 *)
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CROSSREFS
| Column m=1: 2*A142964; m=3: 8*A142966.
Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), Feb 20 2009: (Start)
Cf. A156925
Equals A156920(n+2,2)
Equals A156919(n+2,2)/2^n
(End)
Sequence in context: A056125 A027566 A041620 * A058649 A103308 A010824
Adjacent sequences: A142962 A142963 A142964 * A142966 A142967 A142968
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KEYWORD
| nonn,easy
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AUTHOR
| Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de) Sep 15 2008
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