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A100828
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Expansion of (1+2*x-2*x^3-3*x^2)/((x-1)*(x+1)*(x^2+2*x-1)).
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11
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1, 4, 7, 18, 41, 100, 239, 578, 1393, 3364, 8119, 19602, 47321, 114244, 275807, 665858, 1607521, 3880900, 9369319, 22619538, 54608393, 131836324, 318281039, 768398402, 1855077841, 4478554084, 10812186007, 26102926098, 63018038201
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OFFSET
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0,2
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COMMENTS
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A floretion-generated sequence relating NSW and Pell numbers.
Elements of odd index in the sequence gives A002315. a(n+2) - a(n) = A002203(n+2).
Floretion Algebra Multiplication Program, FAMP Code: 2tesseq[B*C} with B = - .25'i + .25'j + .5'k - .25i' + .25j' + .5k' - .5'kk' - .25'ik' - .25'jk' - .25'ki' - .25'kj' - .5e and C = + .5'i - .25'j + .25'k + .5i' - .25j' + .25k' - .5'ii' - .25'ij' - .25'ik' - .25'ji' - .25'ki' - .5e
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LINKS
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FORMULA
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a(n) = (u^(n+1)+1)*(v^(n+1)+1)/2 with u = 1+sqrt(2), v = 1-sqrt(2). - Vladeta Jovovic, May 30 2007
G.f.: (1 + 2*x - 3*x^2 - 2*x^3) / ((1 - x)*(1 + x)*(1 - 2*x - x^2)).
a(n) = (1 + (-1)^(1+n) + (1-sqrt(2))^(1+n) + (1+sqrt(2))^(1+n)) / 2.
a(n) = 2*a(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4) for n>3.
(End)
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PROG
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(PARI) Vec((1 + 2*x - 3*x^2 - 2*x^3) / ((1 - x)*(1 + x)*(1 - 2*x - x^2)) + O(x^30)) \\ Colin Barker, Apr 29 2019
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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