A167582 The third left hand column of triangle A167580.

3, 98, 1080, 7568, 40976, 187488, 761600, 2830848, 9821952, 32254464, 101263360, 306229248, 897175552, 2558058496, 7123894272, 19434569728, 52063567872, 137236709376, 356550967296, 914355126272, 2317328842752

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 triangle A167580.

Other left hand columns are A014480, A167581, A168305 and A168306.

Programs

Mathematica

LinearRecurrence[{12, -60, 160, -240, 192, -64}, {3, 98, 1080, 7568, 40976, 187488}, 100] (* G. C. Greubel, Jun 16 2016 *)

Formula

a(n) = 2^n*(14*n^5 - 95*n^4 + 240*n^3 - 280*n^2 + 151*n - 30)/240.

GF(z) = (8*z^3 + 84*z^2 + 62*z + 3)/(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-1).

Extensions

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