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%I #19 Jun 23 2023 06:06:35
%S 1,5,12,26,45,75,112,164,225,305,396,510,637,791,960,1160,1377,1629,
%T 1900,2210,2541,2915,3312,3756,4225,4745,5292,5894,6525,7215,7936,
%U 8720,9537,10421,11340,12330,13357,14459,15600,16820,18081,19425,20812,22286,23805
%N Row sums of the triangle in A199332.
%C a(n) = sum(A199332(n,k): 1 <= k <= n);
%C a(2*n-1) = A015237(n); a(2*n) = A048395(n);
%C a(n+1) = A200252(n).
%H Reinhard Zumkeller, <a href="/A199771/b199771.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (2,1,-4,1,2,-1).
%F G.f. x*( 1+3*x+x^2+x^3 ) / ((1+x)^2*(x-1)^4). - R. J. Mathar, Nov 24 2011
%F a(n) = n*(3+2*n^2+4*n+(-1)^n))/8. - _R. J. Mathar_, Jun 23 2023
%t LinearRecurrence[{2,1,-4,1,2,-1},{1,5,12,26,45,75},50] (* _Harvey P. Dale_, Apr 27 2019 *)
%o (Haskell)
%o a199771 = sum . a199332_row
%o (PARI) a(n)=([0,1,0,0,0,0; 0,0,1,0,0,0; 0,0,0,1,0,0; 0,0,0,0,1,0; 0,0,0,0,0,1; -1,2,1,-4,1,2]^(n-1)*[1;5;12;26;45;75])[1,1] \\ _Charles R Greathouse IV_, Jun 18 2017
%K nonn,easy
%O 1,2
%A _Reinhard Zumkeller_, Nov 23 2011
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