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Row sums of triangle A099605, in which row n equals the inverse Binomial transform of column n of the triangle A034870 of even-indexed rows of Pascal's triangle.
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%I #5 Mar 07 2024 14:04:32

%S 1,4,10,48,116,560,1352,6528,15760,76096,183712,887040,2141504,

%T 10340096,24963200,120532992,290992384,1405035520,3392055808,

%U 16378294272,39540700160,190919389184,460920178688,2225519493120,5372879343616

%N Row sums of triangle A099605, in which row n equals the inverse Binomial transform of column n of the triangle A034870 of even-indexed rows of Pascal's triangle.

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0, 12, 0, -4).

%F a(n) = Pell(n+1)*2^[(n+1)/2]. a(n) = 12*a(n-2) - 4*a(n-4) for n>=4. G.f.: (1+4*x-2*x^2)/(1-12*x^2+4*x^4).

%e Sequence begins: {1*1, 2*2, 5*2, 12*4, 29*4, 70*8, 169*8, 408*16, ...}.

%o (PARI) a(n)=polcoeff((1+4*x-2*x^2)/(1-12*x^2+4*x^4)+x*O(x^n),n)

%Y Cf. A099603, A099605, A034870, A000129.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Oct 25 2004