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A100133 a(n) = Sum_{k=0..floor(n/4)} C(n-2k,2k) * 3^k * 2^(n-4k). 4


%S 1,2,4,8,19,50,136,368,985,2618,6940,18392,48763,129338,343120,910304,

%T 2415025,6406898,16996852,45090728,119620579,317340098,841868632,

%U 2233386320,5924932489,15718204970,41698695820,110622122360

%N a(n) = Sum_{k=0..floor(n/4)} C(n-2k,2k) * 3^k * 2^(n-4k).

%C Binomial transform of 1,1,1,1,4,4,10,10,28,28,76,... (g.f. (1-x)(1+x)^2/(1-2x^2-2x^4)).

%H Seiichi Manyama, <a href="/A100133/b100133.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-4,0,3)

%F G.f.: (1-2x)/((1-2x)^2-3x^4).

%F a(n) = 4*a(n-1) - 4*a(n-2) + 3*a(n-3).

%o (PARI) a(n) = sum(k=0, n\4, binomial(n-2*k,2*k) * 3^k * 2^(n-4*k)); \\ _Michel Marcus_, Oct 09 2021

%Y Cf. A100131, A100132.

%K easy,nonn

%O 0,2

%A _Paul Barry_, Nov 06 2004

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Last modified December 3 17:23 EST 2021. Contains 349467 sequences. (Running on oeis4.)