A154918 - OEIS

%I #8 Sep 08 2022 08:45:40

%S 2,5,5,29,112,29,221,1144,1144,221,1821,12000,16016,12000,1821,15505,

%T 127110,206720,206720,127110,15505,134597,1309528,2838752,2615008,

%U 2838752,1309528,134597,1184041,13126386,37818900,37328655,37328655,37818900,13126386,1184041

%N Triangle, read by rows, T(n, k) = binomial(4*n, 3*k) + binomial(4*n, 3*(n-k)).

%C Row sums are: {2, 10, 170, 2730, 43658, 698670, 11180762, 178915964, 2862907786,

%C 45809074626, 732970281870, ...}.

%H G. C. Greubel, <a href="/A154918/b154918.txt">Rows n = 0..100 of triangle, flattened</a>

%F T(n, k) = binomial(4*n, 3*k) + binomial(4*n, 3*(n-k)).

%e Triangle begins as:

%e       2;

%e       5,      5;

%e      29,    112,     29;

%e     221,   1144,   1144,    221;

%e    1821,  12000,  16016,  12000,   1821;

%e   15505, 127110, 206720, 206720, 127110, 15505;

%p b:=binomial; seq(seq( b(4*n, 3*k) + b(4*n, 3*(n-k)), k=0..n), n=0..10); # _G. C. Greubel_, Dec 02 2019

%t Table[Binomial[4*n, 3*k] +Binomial[4*n, 3*(n-k)], {n,0,10}, {k,0,n}]//Flatten (* modified by _G. C. Greubel_, Dec 02 2019 *)

%o (PARI) T(n,k) = my(b=binomia); b(4*n, 3*k) + b(4*n, 3*(n-k)); \\ _G. C. Greubel_, Dec 02 2019

%o (Magma) B:=Binomial; [B(4*n, 3*k) + B(4*n, 3*(n-k)): k in [0..n], n in [0..10]]; // _G. C. Greubel_, Dec 02 2019

%o (Sage) b=binomial; [[b(4*n, 3*k) + b(4*n, 3*(n-k)) for k in (0..n)] for n in (0..10)] # _G. C. Greubel_, Dec 02 2019

%o (GAP) B:=Binomial;; Flat(List([0..10], n-> List([0..n], k-> B(4*n, 3*k) + B(4*n, 3*(n-k)) ))); # _G. C. Greubel_, Dec 02 2019

%K nonn,tabl

%O 0,1

%A _Roger L. Bagula_, Jan 17 2009

%E Edited by _G. C. Greubel_, Dec 02 2019