A024042 a(n) = 4^n - n^6.

1, 3, -48, -665, -3840, -14601, -42560, -101265, -196608, -269297, 48576, 2422743, 13791232, 62282055, 260905920, 1062351199, 4278190080, 17155731615, 68685464512, 274830861063, 1099447627776

Offset: 0

Author

N. J. A. Sloane

Keywords

• sign
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..500
• Index entries for linear recurrences with constant coefficients, signature (11, -49, 119, -175, 161, -91, 29, -4).

Programs

Magma

[4^n-n^6: n in [0..30]]; // Vincenzo Librandi, Jul 02 2011

Mathematica

Table[4^n-n^6,{n,0,30}] (* or *) LinearRecurrence[ {11,-49,119,-175,161,-91,29,-4},{1,3,-48,-665,-3840,-14601,-42560,-101265},30] (* Harvey P. Dale, Jun 25 2013 *)

Formula

a(n) = 11*a(n-1) - 49*a(n-2) + 119*a(n-3) - 175*a(n-4) + 161*a(n-5) - 91*a(n-6) + 29*a(n-7) - 4*a(n-8); a(0)=1, a(1)=3, a(2)=-48, a(3)=-665, a(4)=-3840, a(5)=-14601, a(6)=-42560, a(7)=-101265. - Harvey P. Dale, Jun 25 2013