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Expansion of (1+x)*(1+2*x)*(1-x)/(1-5*x^2+5*x^4).
4

%I #17 Oct 02 2023 13:47:00

%S 1,2,4,8,15,30,55,110,200,400,725,1450,2625,5250,9500,19000,34375,

%T 68750,124375,248750,450000,900000,1628125,3256250,5890625,11781250,

%U 21312500,42625000,77109375,154218750,278984375,557968750,1009375000,2018750000,3651953125

%N Expansion of (1+x)*(1+2*x)*(1-x)/(1-5*x^2+5*x^4).

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0, 5, 0, -5).

%F a(n) = A216212(n+1)/2.

%F a(2n) = A039717(n+1), a(2n+1) = 2*a(2n) = 2*A039717(n+1).

%F a(n) = sum(A217770(n-k,k), 0<=k<=n).

%F a(n) = 5*a(n-2) - 5*a(n-4) for n>=4, a(0) = 1, a(1) = 2, a(2) = 4, a(3) = 8.

%F G.f.: (1+x)*(1+2*x)*(1-x)/(1-5*x^2+5*x^4).

%o (PARI) Vec((1+x)*(1+2*x)*(1-x)/(1-5*x^2+5*x^4)+O(x^66)) /* _Joerg Arndt_, Mar 29 2013 */

%Y Cf. A217770

%K nonn,easy

%O 0,2

%A _Philippe Deléham_, Mar 24 2013

%E Corrected name (g.f.), _Joerg Arndt_, Mar 29 2013