A101496 Expansion of (1-x^2)/(1-x-x^2+x^3+x^4).

1, 1, 1, 1, 0, -1, -3, -5, -7, -8, -7, -3, 5, 17, 32, 47, 57, 55, 33, -16, -95, -199, -311, -399, -416, -305, -11, 499, 1209, 2024, 2745, 3061, 2573, 865, -2368, -7137, -12943, -18577, -22015, -20512, -11007, 9073, 40593, 81185, 123712, 155231, 157165, 107499, -14279, -219176

Offset

0,7

Comments

Results from applying a Chebyshev transform after an inverse Catalan transform to 1/(1-x). 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

Muniru A Asiru, Table of n, a(n) for n = 0..5000

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

Formula

a(n) = a(n-1) +a(n-2) -a(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).

Mathematica

CoefficientList[Series[(1-x^2)/(1-x-x^2+x^3+x^4), {x, 0, 50}], x] (* or *) LinearRecurrence[{1, 1, -1, -1}, {1, 1, 1, 1}, 50] (* Harvey P. Dale, Jun 05 2012 *)

Prog

(GAP) a:=[1, 1, 1, 1];; for n in [5..50] do a[n]:=a[n-1]+a[n-2]-a[n-3]-a[n-4]; od; Print(a); # Muniru A Asiru, Mar 04 2019
(PARI) my(x='x+O('x^50)); Vec((1-x^2)/(1-x-x^2+x^3+x^4)) \\ G. C. Greubel, Mar 05 2019
(Magma) I:=[1, 1, 1, 1]; [n le 4 select I[n] else Self(n-1) +Self(n-2) - Self(n-3) -Self(n-4): n in [1..50]]; // G. C. Greubel, Mar 05 2019
(Sage) ((1-x^2)/(1-x-x^2+x^3+x^4)).series(x, 50).coefficients(x, sparse=False) # G. C. Greubel, Mar 05 2019

Crossrefs

Sequence in context: A185168 A131979 A335894 * A218490 A161696 A196084

Adjacent sequences: A101493 A101494 A101495 * A101497 A101498 A101499

Keyword

easy,sign

Author

Paul Barry, Dec 04 2004

Status

approved