A167593 The third left hand column of triangle A167591.

9, 120, 952, 5664, 27888, 120064, 467712, 1686528, 5719296, 18450432, 57108480, 170713088, 495366144, 1401028608, 3874881536, 10508304384, 28005433344, 73485778944, 190154539008, 485895438336, 1227495571456

Offset: 3

Author

Johannes W. Meijer, Nov 10 2009

Keywords

• easy
• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 3..1000
• Index entries for linear recurrences with constant coefficients, signature (12,-60,160,-240,192,-64).

Crossrefs

Equals the third left hand column of A167591.

Other left hand columns are A001787, A167592, A168307 and A168308.

Programs

Mathematica

LinearRecurrence[{12,-60,160,-240,192,-64},{9, 120, 952, 5664, 27888, 120064},100] (* G. C. Greubel, Jun 17 2016 *)

Formula

a(n) = 2^n*(7*n^5 - 40*n^4 + 110*n^3 - 155*n^2 + 78*n)/240.

GF(z) = (52*z^2 + 12*z + 9)/(1-2*z)^6.

a(n) = 12*a(n-1) - 60*a(n-2) + 160*a(n-3) - 240*a(n-4) + 192*a(n-5) - 64*a(n-6).

a(n) - 11*a(n-1) + 50*a(n-2) - 120*a(n-3) + 160*a(n-4) - 112*a(n-5) + 32*a(n-6) = 7*2^(n-2).

Extensions

Formulae and links added by Johannes W. Meijer, Nov 23 2009