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a(n) is the n-th diagonal sum of left justified array T given by A027960.
1

%I #16 Sep 08 2022 08:44:49

%S 1,1,4,5,8,12,16,23,31,42,57,76,102,136,181,241,320,425,564,748,992,

%T 1315,1743,2310,3061,4056,5374,7120,9433,12497,16556,21933,29056,

%U 38492,50992,67551,89487,118546,157041,208036,275590,365080,483629,640673,848712,1124305,1489388,1973020

%N a(n) is the n-th diagonal sum of left justified array T given by A027960.

%H G. C. Greubel, <a href="/A027975/b027975.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 (1,1,0,-1).

%F G.f.: (1 + 2*x^2)/((1-x)*(1-x^2-x^3)).

%F a(n) = a(n-2) + a(n-3) + 3. - _Greg Dresden_, May 18 2020

%p seq(coeff(series((1+2*x^2)/((1-x)*(1-x^2-x^3)), x, n+1), x, n), n = 0..40); # _G. C. Greubel_, Sep 26 2019

%t CoefficientList[Series[(1+2*x^2)/((1-x)*(1-x^2-x^3)), {x,0,40}], x] (* or *) LinearRecurrence[{1,1,0,-1}, {1,1,4,5}, 41] (* _G. C. Greubel_, Sep 26 2019 *)

%o (PARI) my(x='x+O('x^40)); Vec((1+2*x^2)/((1-x)*(1-x^2-x^3))) \\ _G. C. Greubel_, Sep 26 2019

%o (Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1+2*x^2)/((1-x)*(1-x^2-x^3)) )); // _G. C. Greubel_, Sep 26 2019

%o (Sage)

%o def A027975_list(prec):

%o P.<x> = PowerSeriesRing(ZZ, prec)

%o return P( (1+2*x^2)/((1-x)*(1-x^2-x^3)) ).list()

%o A027975_list(40) # _G. C. Greubel_, Sep 26 2019

%o (GAP) a:=[1,1,4,5];; for n in [5..40] do a[n]:=a[n-1]+a[n-2]-a[n-4]; od; a; # _G. C. Greubel_, Sep 26 2019

%Y Cf. A027960.

%K nonn

%O 0,3

%A _Clark Kimberling_

%E Terms a(32) onward added by _G. C. Greubel_, Sep 26 2019