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A transform of the Pell numbers.
1

%I #8 Jun 13 2015 00:51:33

%S 0,1,2,5,10,23,50,112,246,545,1202,2658,5870,12972,28656,63315,139880,

%T 309049,682790,1508527,3332850,7363430,16268356,35942447,79409300,

%U 175442668,387613604,856372740,1892023992,4180136405,9235369230

%N A transform of the Pell numbers.

%C A transform of A000129 under the mapping g(x)->(1/(1+x^3))g(x/(1+x^3))

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (2,1,-2,2,0,-1).

%F G.f.: x/(1-2x-x^2+2x^3-2x^4+x^6); a(n)=2a(n-1)+a(n-2)-2a(n-3)+2a(n-4)-a(n-6); a(n)=sum{k=0..floor(n/3), binomial(n-2k, k)(-1)^k*Pell(n-3k)}.

%t LinearRecurrence[{2,1,-2,2,0,-1},{0,1,2,5,10,23},40] (* _Harvey P. Dale_, Apr 15 2015 *)

%Y Cf. A099505, A099508.

%K easy,nonn

%O 0,3

%A _Paul Barry_, Oct 20 2004