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A101498
Expansion of (1-x^2)/(1-3x+x^2+3x^3+x^4).
0
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
OFFSET
0,2
COMMENTS
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)).
FORMULA
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)}}.
MATHEMATICA
LinearRecurrence[{3, -1, -3, -1}, {1, 3, 7, 15}, 34] (* James C. McMahon, Jan 01 2024 *)
CROSSREFS
Sequence in context: A350370 A103021 A025587 * A027965 A130145 A023552
KEYWORD
easy,sign
AUTHOR
Paul Barry, Dec 04 2004
STATUS
approved