OFFSET
0,3
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..230
Index entries for linear recurrences with constant coefficients, signature (8,-27,50,-55,36,-13,2).
FORMULA
G:f.: (1-7*x-9*x^2-34*x^3+121*x^4+45*x^5+3*x^6) / ((1-2*x)*(1-x)^6). - Vincenzo Librandi, Oct 07 2014
a(n) = 8*a(n-1) -27*a(n-2) +50*a(n-3) -55*a(n-4) +36*a(n-5) -13*a(n-6) +2*a(n-7) for n>6. - Vincenzo Librandi, Oct 07 2014
MATHEMATICA
Table[2^n - n^5, {n, 0, 30}] (* or *) CoefficientList[Series[(1 - 7 x - 9 x^2 - 34 x^3 + 121 x^4 + 45 x^5 + 3 x^6)/((1 - 2 x) (1 - x)^6), {x, 0, 30}], x] (* Vincenzo Librandi, Oct 07 2014 *)
LinearRecurrence[{8, -27, 50, -55, 36, -13, 2}, {1, 1, -28, -235, -1008, -3093, -7712}, 30] (* Harvey P. Dale, May 14 2016 *)
PROG
(Magma) [2^n-n^5: n in [0..35]]; // Vincenzo Librandi, Apr 29 2011
(Magma) I:=[1, 1, -28, -235, -1008, -3093, -7712]; [n le 7 select I[n] else 8*Self(n-1)-27*Self(n-2)+50*Self(n-3)-55*Self(n-4)+36*Self(n-5)-13*Self(n-6)+2*Self(n-7): n in [1..35]]; // Vincenzo Librandi, Oct 07 2014
CROSSREFS
KEYWORD
sign,easy
AUTHOR
STATUS
approved