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Search: id:A114654
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| A114654 |
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Discriminant of the polynomial x^n + x + 1. |
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+0
1
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| 1, -3, -31, 229, 3381, -43531, -870199, 15953673, 404197705, -9612579511, -295311670611, 8630788777645, 311791207040509, -10809131718965763, -449005897206417391, 18008850183328692241, 845687005960046315793, -38519167813410200811247
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OFFSET
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1,2
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COMMENT
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Except for the sign, the sequence alternates between the sum and difference of consecutive terms of A000312. x^2+x+1 divides x^n+x+1 for n=2 (mod 3).
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FORMULA
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for n>1, a(n) = (n^n + (-1)^(n-1) (n-1)^(n-1)) (-1)^floor(n/2)
a(n) = (Cos[Pi n/2]+Sin[Pi n/2])(n^n)+(Cos[Pi(n+1)/2]+Sin[Pi(n+1)/2])(n+1)^(n+1) - Artur Jasinski (grafix(AT)csl.pl), Oct 12 2007
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MATHEMATICA
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1) Table[(Cos[Pi n/2] + Sin[Pi n/2])(n)^(n)(1)^(n + 1) + (Cos[Pi (n + 1)/2] + Sin[Pi (n + 1)/2])(n + 1)^(n + 1), {n, 1, 100}] 2) Table[Discriminant[x^n + x + 1, x], {n, 0, 100}] - Artur Jasinski (grafix(AT)csl.pl), Oct 12 2007
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CROSSREFS
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Cf. A000312 (n^n), A007781 (n^n - (n-1)^(n-1)), A056788 (n^n + (n-1)^(n-1)), A086797 (discriminant of the polynomial x^n-x-1).
Sequence in context: A060425 A121099 A121147 this_sequence A111400 A057972 A114849
Adjacent sequences: A114651 A114652 A114653 this_sequence A114655 A114656 A114657
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KEYWORD
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sign
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AUTHOR
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T. D. Noe (noe(AT)sspectra.com), Dec 21 2005
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