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Search: id:A101498
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| A101498 |
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Expansion of (1-x^2)/(1-3x+x^2+3x^3+x^4). |
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+0
1
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| 1, 3, 7, 15, 28, 45, 55, 21, -155, -696, -2051, -5013, -10745, -20373, -33284, -42231, -21545, 97821, 474985, 1434000, 3555097, 7708515, 14793463, 24572583, 32243644, 20069445, -60546521, -323012523, -1000943027, -2518246440, -5524212203, -10728548565, -18105751145, -24497821821
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Results from applying a Chebyshev transform after an inverse Catalan transform to 1/(1-3x). The inverse Catalan transform maps g(x)->g(x(1-x)) while the Chebyshev transform maps h(x)->(1/(1+x^2))h(x/(1+x^2)).
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FORMULA
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a(n)=3a(n-1)-a(n-2)-3a(n-3)-a(n-4); a(n)=sum{k=0..floor(n/2), sum{j=0..floor((n-2k)/2), C(n-k, k)C(n-2k-j, j)3^(n-2k-j)}}.
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CROSSREFS
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Sequence in context: A147394 A103021 A025587 this_sequence A027965 A130145 A023552
Adjacent sequences: A101495 A101496 A101497 this_sequence A101499 A101500 A101501
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KEYWORD
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easy,sign
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Dec 04 2004
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