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A138238 Alternating sum of the squares of the first n Jacobsthal numbers. 1

%I

%S 0,1,0,9,-16,105,-336,1513,-5712,23529,-92752,373737,-1489488,5968873,

%T -23853648,95458281,-381745744,1527157737,-6108281424,24433824745,

%U -97733900880,390938399721,-1563748006480

%N Alternating sum of the squares of the first n Jacobsthal numbers.

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (-2,9,2,-8).

%F G.f. : x(1+2x)/((1-x^2)(1+2x-8x^2));

%F a(n)=4*2^n/9-4(-4)^n/45-(-1)^n/18-3/10;

%F a(n)=(13-4*J(2n+1))(-1)^n/30+4*J(n)/3-3/10, J(n)=A001045(n);

%F a(n)=sum{k=0..n (-1)^(k+1)*J(k)^2};

%t LinearRecurrence[{-2,9,2,-8},{0,1,0,9},30] (* _Harvey P. Dale_, Feb 13 2018 *)

%Y Cf. A119283.

%K easy,sign

%O 0,4

%A _Paul Barry_, Mar 07 2008

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Last modified January 23 21:06 EST 2022. Contains 350515 sequences. (Running on oeis4.)