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A027947 a(n) = Sum_{k=m..n} T(k,n-k), where m = floor((n+1)/2); a(n) is the n-th diagonal-sum of left justified array T given by A027935.

%I A027947 #14 Sep 08 2022 08:44:49
%S A027947 1,1,2,3,4,7,9,15,21,32,48,70,107,156,236,349,521,778,1155,1728,2567,
%T A027947 3833,5707,8505,12680,18884,28158,41943,62520,93160,138825,206897,
%U A027947 308290,459459,684652,1020311,1520473,2265815,3376605
%N A027947 a(n) = Sum_{k=m..n} T(k,n-k), where m = floor((n+1)/2); a(n) is the n-th diagonal-sum of left justified array T given by A027935.
%H A027947 G. C. Greubel, <a href="/A027947/b027947.txt">Table of n, a(n) for n = 0..1000</a>
%H A027947 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,2,1,-1).
%F A027947 G.f.: (1 + x)/(1 - 2*x^2 - x^3 + x^4).
%p A027947 seq(coeff(series((1+x)/(1-2*x^2-x^3+x^4), x, n+1), x, n), n = 0..40); # _G. C. Greubel_, Sep 29 2019
%t A027947 LinearRecurrence[{0,2,1,-1}, {1,1,2,3}, 40] (* _G. C. Greubel_, Sep 29 2019 *)
%o A027947 (PARI) my(x='x+O('x^40)); Vec((1+x)/(1-2*x^2-x^3+x^4)) \\ _G. C. Greubel_, Sep 29 2019
%o A027947 (Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1+x)/(1-2*x^2-x^3+x^4) )); // _G. C. Greubel_, Sep 29 2019
%o A027947 (Sage)
%o A027947 def A027947_list(prec):
%o A027947     P.<x> = PowerSeriesRing(ZZ, prec)
%o A027947     return P((1+x)/(1-2*x^2-x^3+x^4)).list()
%o A027947 A027947_list(40) # _G. C. Greubel_, Sep 29 2019
%o A027947 (GAP) a:=[1,1,2,3];; for n in [5..40] do a[n]:=2*a[n-2]+a[n-3]-a[n-4]; od; a; # _G. C. Greubel_, Sep 29 2019
%Y A027947 Cf. A027935.
%K A027947 nonn
%O A027947 0,3
%A A027947 _Clark Kimberling_