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A174301 A symmetrical triangle: T(n,k) = binomial(n, k)*if(floor(n/2) greater than or equal to k then 4^k, otherwise 4^(n-k)).

%I A174301 #8 Sep 08 2022 08:45:51
%S A174301 1,1,1,1,8,1,1,12,12,1,1,16,96,16,1,1,20,160,160,20,1,1,24,240,1280,
%T A174301 240,24,1,1,28,336,2240,2240,336,28,1,1,32,448,3584,17920,3584,448,32,
%U A174301 1,1,36,576,5376,32256,32256,5376,576,36,1,1,40,720,7680,53760,258048,53760,7680,720,40,1
%N A174301 A symmetrical triangle: T(n,k) = binomial(n, k)*if(floor(n/2) greater than or equal to k then 4^k, otherwise 4^(n-k)).
%C A174301 Row sums are: {1, 2, 10, 26, 130, 362, 1810, 5210, 26050, 76490, ...}.
%H A174301 G. C. Greubel, <a href="/A174301/b174301.txt">Rows n = 0..100 of triangle, flattened</a>
%F A174301 T(n, m) = binomial(n, m)*if(floor(n/2) greater than or equal to m then 4^m, otherwise 4^(n-m)).
%e A174301 Triangle begins:
%e A174301   1;
%e A174301   1,  1;
%e A174301   1,  8,   1;
%e A174301   1, 12,  12,    1;
%e A174301   1, 16,  96,   16,     1;
%e A174301   1, 20, 160,  160,    20,      1;
%e A174301   1, 24, 240, 1280,   240,     24,     1;
%e A174301   1, 28, 336, 2240,  2240,    336,    28,    1;
%e A174301   1, 32, 448, 3584, 17920,   3584,   448,   32,   1;
%e A174301   1, 36, 576, 5376, 32256,  32256,  5376,  576,  36,  1;
%e A174301   1, 40, 720, 7680, 53760, 258048, 53760, 7680, 720, 40,  1;
%t A174301 Table[Binomial[n, m]*If[Floor[n/2]>=m , 4^m, 4^(n-m)], {n,0,10}, {m,0,n} ]//Flatten
%o A174301 (PARI) {T(n,k) = binomial(n,k)*if(floor(n/2)>=k, 4^k, 4^(n-k))}; \\ _G. C. Greubel_, Apr 15 2019
%o A174301 (Magma) [[Floor(n/2) ge k select 4^k*Binomial(n,k) else 4^(n-k)*Binomial(n,k): k in [0..n]]: n in [0..10]]; // _G. C. Greubel_, Apr 15 2019
%o A174301 (Sage)
%o A174301 def T(n,k):
%o A174301    if floor(n/2)>=k: return 4^k*binomial(n,k)
%o A174301    else: return 4^(n-k)*binomial(n,k)
%o A174301 [[T(n,k) for k in (0..n)] for n in (0..10)] # _G. C. Greubel_, Apr 15 2019
%Y A174301 Cf. A144463, A144470.
%Y A174301 T(2n,n) gives A098430.
%K A174301 nonn,tabl
%O A174301 0,5
%A A174301 _Roger L. Bagula_, Mar 15 2010
%E A174301 Edited by _G. C. Greubel_, Apr 15 2019