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Search: id:A143462
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| A143462 |
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Expansion of 1 / (1 + 4 * x + 8 * x^2) in powers of x. |
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+0
1
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| 1, -4, 8, 0, -64, 256, -512, 0, 4096, -16384, 32768, 0, -262144, 1048576, -2097152, 0, 16777216, -67108864, 134217728, 0, -1073741824, 4294967296, -8589934592, 0, 68719476736, -274877906944, 549755813888, 0, -4398046511104, 17592186044416
(list; graph; listen)
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OFFSET
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0,2
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FORMULA
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G.f.: 1 / (1 + 4 * x + 8 * x^2). E.g.f: (cos(2 * x) - sin(2 * x)) / exp(2 * x).
a(n) = -4 * a(n-1) - 8 * a(n-2). a(n+4) = -64 * a(n).
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EXAMPLE
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1 - 4*x + 8*x^2 - 64*x^4 + 256*x^5 - 512*x^6 + 4096*x^8 - 16384*x^9 + ...
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PROGRAM
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(PARI) {a(n) = (-64)^(n \ 4) * [1, -4, 8, 0][n%4 + 1]}
(PARI) {a(n) = n--; -2 * 2^n * ((-1 + I)^n + (-1 - I)^n)}
(PARI) {a(n) = n--; simplify( -4 * (2 * quadgen(8))^n * polchebyshev(n, 1, -1 / quadgen(8)))}
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CROSSREFS
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A030210(2^n) = 2^n * A108520(n) = a(n).
Sequence in context: A104538 A120580 A013328 this_sequence A042972 A021875 A127734
Adjacent sequences: A143459 A143460 A143461 this_sequence A143463 A143464 A143465
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KEYWORD
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sign
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AUTHOR
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Michael Somos, Aug 16 2008
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