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A024015
2^n-n^5.
2
1, 1, -28, -235, -1008, -3093, -7712, -16679, -32512, -58537, -98976, -159003, -244736, -363101, -521440, -726607, -983040, -1288785, -1627424, -1951811, -2151424, -1986949, -959328, 1952265, 8814592, 23788807, 55227488, 119868821, 251225088
OFFSET
0,3
LINKS
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
Cf. sequences of the form k^n-n^5: this sequence (k=2), A024028 (k=3), A024041 (k=4), A024054 (k=5), A024067 (k=6), A024080 (k=7), A024093 (k=8), A024106 (k=9), A024119 (k=10), A024132 (k=11), A024145 (k=12).
Sequence in context: A115224 A135497 A138405 * A223347 A242436 A119544
KEYWORD
sign,easy
AUTHOR
STATUS
approved