A167581 The second left hand column of triangle A167580.

-1, 0, 28, 192, 880, 3328, 11200, 34816, 102144, 286720, 777216, 2048000, 5271552, 13303808, 33013760, 80740352, 194969600, 465567744, 1100742656, 2579496960, 5996806144, 13841203200, 31738298368, 72343355392, 163997286400

Offset: 2

Author

Johannes W. Meijer, Nov 10 2009

Keywords

• easy
• sign

Links

• G. C. Greubel, Table of n, a(n) for n = 2..1000
• Index entries for linear recurrences with constant coefficients, signature (8, -24, 32, -16).

Crossrefs

Equals the second left hand column of triangle A167580.

Other left hand columns are A014480 A167582, A168305 and A168306.

Programs

Mathematica

LinearRecurrence[{8,-24,32,-16},{-1,0,28,192},30] (* Harvey P. Dale, Jan 22 2012 *)

Formula

a(n) = 2^n*(2*n^3 - 9*n^2 + 10*n - 3)/12.

GF(z) = (4*z^2 + 8*z - 1)/(1-2*z)^4.

a(n) = 8*a(n-1) - 24*a(n-2) + 32*a(n-3) - 16*a(n-4)

a(n) - 7*a(n-1) + 18*a(n-2) - 20*a(n-3) + 8*a(n-4) = 1*2^(n-1)

Extensions

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