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A154223 Diagonal sums of number triangle A154221.

%I A154223 #21 Sep 08 2022 08:45:40
%S A154223 1,1,2,3,5,9,16,32,61,125,246,502,999,2023,4040,8136,16265,32649,
%T A154223 65290,130826,261643,523787,1047564,2096140,4192269,8386573,16773134,
%U A154223 33550350,67100687,134209551,268419088,536854544,1073709073,2147450897,4294901778,8589869074,17179738131,34359607315,68719214612,137438691348
%N A154223 Diagonal sums of number triangle A154221.
%H A154223 G. C. Greubel, <a href="/A154223/b154223.txt">Table of n, a(n) for n = 0..1000</a>
%H A154223 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (3,1,-9,4,6,-4).
%F A154223 G.f.: (1 - x - x^2)*(1 - x - 2*x^2 + 2*x^3 - x^4) / ((1-x)^2*(1+x)*(1-2*x)*(1-2*x^2)). - _Colin Barker_, Sep 07 2016
%p A154223 A154223 := proc(n)
%p A154223     a := 0 ;
%p A154223     for npr from n by -1 do
%p A154223         k := n-npr ;
%p A154223         if k <= npr then
%p A154223             a := a+A154221(npr,k) ;
%p A154223         else
%p A154223             return a;
%p A154223         end if;
%p A154223     end do:
%p A154223 end proc: # _R. J. Mathar_, Feb 05 2015
%t A154223 Join[{1}, LinearRecurrence[{3, 1, -9, 4, 6, -4}, {1, 2, 3, 5, 9, 16}, 25]] (* _G. C. Greubel_, Sep 06 2016 *)
%o A154223 (Magma) I:=[1,1,2,3,5,9,16]; [n le 7 select I[n] else 3*Self(n-1)+Self(n-2)-9*Self(n-3)+4*Self(n-4)+6*Self(n-5)-4*Self(n-6): n in [1..40]]; // _Vincenzo Librandi_, Sep 07 2016
%o A154223 (PARI) Vec((1-x-x^2)*(1-x-2*x^2+2*x^3-x^4)/((1-x)^2*(1+x)*(1-2*x)*(1-2*x^2)) + O(x^40)) \\ _Colin Barker_, Sep 07 2016
%K A154223 nonn,easy
%O A154223 0,3
%A A154223 _Paul Barry_, Jan 05 2009