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%I #6 Sep 08 2022 08:45:24
%S 1,4,17,76,337,1496,6641,29480,130865,580924,2578785,11447508,
%T 50816737,225581040,1001378849,4445229968,19732860833,87596322228,
%U 388849631729,1726145941404,7662550168241,34014896233544,150995835638929,670286989081400,2975477077435217,13208467391670124,58633827885912001,260281959337906852
%N Expansion of (1-x^2)/(1 -4*x -2*x^2 +x^4).
%C Row sums of unsigned version of number triangle A117438.
%H G. C. Greubel, <a href="/A117439/b117439.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 (4,2,0,-1).
%F a(n) = 4*a(n-1) + 2*a(n-2) - a(n-4).
%F a(n) = Sum_{k=0..floor(n/2)} binomial(2*n-3*k, k) * 4^(n-2*k).
%t LinearRecurrence[{4,2,0,-1}, {1,4,17,76}, 40] (* _G. C. Greubel_, Jun 01 2021 *)
%o (Magma) I:=[1,4,17,76]; [n le 4 select I[n] else 4*Self(n-1) +2*Self(n-2) -Self(n-4): n in [1..41]]; // _G. C. Greubel_, Jun 01 2021
%o (Sage)
%o def A117439_list(prec):
%o P.<x> = PowerSeriesRing(ZZ, prec)
%o return P( (1-x^2)/(1-4*x-2*x^2+x^4) ).list()
%o A117439_list(40) # _G. C. Greubel_, Jun 01 2021
%Y Cf. A117438.
%K easy,nonn
%O 0,2
%A _Paul Barry_, Mar 16 2006
%E Terms a(23) onward added by _G. C. Greubel_, Jun 01 2021
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