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Row sums of the triangle in A199332.
9

%I #24 Oct 24 2024 03:50:16

%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_{k=1..n} A199332(n,k);

%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