A123003 Expansion of g.f.: (8-29*x+24*x^2)/((1-4*x)*(1-3*x)*(1-2*x)^2*(1-x)^2).
8, 75, 463, 2394, 11274, 50265, 216581, 912648, 3788560, 15565095, 63484779, 257591862, 1041276566, 4197718965, 16888451857, 67845945636, 272258886492, 1091657974275, 4374492890615, 17521540911570, 70156842333538, 280839342481425, 1123993155149853
Offset: 0
Links
- G. C. Greubel, Table of n, a(n) for n = 0..1000
- E. Rodney Canfield and Herbert S. Wilf, Counting permutations by their runs up and down, arXiv:math/0609704 [math.CO], 2006; See u_4.
- Index entries for linear recurrences with constant coefficients, signature (13,-67,175,-244,172,-48).
Programs
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Magma
[(2*n + 3 - (n-1)*2^(n+4) - 3^(n+5) + 4^(n+4))/4: n in [0..30]]; // G. C. Greubel, Jul 12 2021
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Mathematica
LinearRecurrence[{13, -67, 175, -244, 172, -48}, {8, 75, 463, 2394, 11274, 50265}, 23] (* Jean-François Alcover, Oct 08 2018 *) -
Sage
[(2*n + 3 - (n-1)*2^(n+4) - 3^(n+5) + 4^(n+4))/4 for n in [0..30]] # G. C. Greubel, Jul 12 2021
Formula
a(n) = (2*(n+1) + 1 - 16*(n-1)*2^n - 243*3^n + 64*4^(n+1))/4. - Greg Dresden, Jun 21 2021