A101498 Expansion of (1-x^2)/(1-3x+x^2+3x^3+x^4).

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)).

Links

Table of n, a(n) for n=0..33.

Index entries for linear recurrences with constant coefficients, signature (3,-1,-3,-1)

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

Adjacent sequences: A101495 A101496 A101497 * A101499 A101500 A101501

Keyword

easy,sign

Author

Paul Barry, Dec 04 2004

Status

approved