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A177825
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Expansion of 1/((1 + x^3 - x^4)*(1 - x)).
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1
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1, 1, 1, 0, 1, 1, 2, 0, 1, 0, 3, 0, 2, -2, 4, -1, 5, -5, 6, -5, 11, -10, 12, -15, 22, -21, 28, -36, 44, -48, 65, -79, 93, -112, 145, -171, 206, -256, 317, -376, 463, -572, 694, -838, 1036, -1265, 1533, -1873, 2302, -2797, 3407
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OFFSET
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0,7
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COMMENTS
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Limiting ratio a(n+1)/a(n) is -1.2207440846057594..., which is a root of z^4 + z - 1.
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LINKS
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FORMULA
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Recurrence a(i)= a(i-1) - a(i-3) + 2 a(i-4) - a(i-5).
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MAPLE
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N:= 100: # to get terms up to index N
for i from 0 to 4 do a[i]:= coeftayl(1/(1+x^3-x^4)/(1-x), x=0, i) end do:
for i from 5 to N do a[i]:= a[i-1] - a[i-3] + 2*a[i-4] - a[i-5] end do:
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MATHEMATICA
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CoefficientList[ Series[1/(1 - x + x^3 - 2 x^4 + x^5), {x, 0, 50}], x] (* Or *)
LinearRecurrence[{1, 0, -1, 2, -1}, {1, 1, 1, 0, 1}, 51] (* Robert G. Wilson v, Feb 11 2013 *)
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CROSSREFS
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KEYWORD
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sign,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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