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

0,1

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).

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

Mathematica

LinearRecurrence[{13, -67, 175, -244, 172, -48}, {8, 75, 463, 2394, 11274, 50265}, 23] (* Jean-François Alcover, Oct 08 2018 *)

Prog

(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
(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

Crossrefs

Cf. A000352, A059427, A060158.

Sequence in context: A166084 A123661 A288487 * A015578 A145600 A268085

Adjacent sequences: A123000 A123001 A123002 * A123004 A123005 A123006

Keyword

nonn,easy

Author

N. J. A. Sloane, Nov 09 2006

Status

approved