%I #7 Jan 09 2022 02:30:09
%S 1,1,1,1,4,1,1,9,9,1,1,16,48,16,1,1,33,97,97,33,1,1,64,192,640,192,64,
%T 1,1,129,385,1281,1281,385,129,1,1,256,768,2560,7168,2560,768,256,1,1,
%U 513,1537,5121,14337,14337,5121,1537,513,1,1,1024,3072,10240,28672,90112,28672,10240,3072,1024,1
%N Triangle T(n, k) = 2^(n+k-2)*prime(k) + (n mod 2) if k <= floor(n/2) otherwise 2^(2*n-k-2)*prime(n-k) + (n mod 2), with T(n, 0) = T(n, n) = 1, read by rows.
%H G. C. Greubel, <a href="/A157192/b157192.txt">Rows n = 0..50 of the triangle, flattened</a>
%F T(n, k) = 2^(n+k-2)*prime(k) + (n mod 2) if k <= floor(n/2) otherwise 2^(2*n-k-2)*prime(n-k) + (n mod 2), with T(n, 0) = T(n, n) = 1.
%F T(n, n-k) = T(n, k).
%e Triangle begins as:
%e 1;
%e 1, 1;
%e 1, 4, 1;
%e 1, 9, 9, 1;
%e 1, 16, 48, 16, 1;
%e 1, 33, 97, 97, 33, 1;
%e 1, 64, 192, 640, 192, 64, 1;
%e 1, 129, 385, 1281, 1281, 385, 129, 1;
%e 1, 256, 768, 2560, 7168, 2560, 768, 256, 1;
%e 1, 513, 1537, 5121, 14337, 14337, 5121, 1537, 513, 1;
%e 1, 1024, 3072, 10240, 28672, 90112, 28672, 10240, 3072, 1024, 1;
%t f[n_, k_]:= Prime[k]*2^(n+k-2) + Mod[n,2];
%t T[n_, k_]:= If[k==0 || k==n, 1, If[k<=Floor[n/2], f[n, k], f[n, n-k] ]];
%t Table[T[n, k], {n,0,10}, {k,0,n}]//Flatten (* modified by _G. C. Greubel_, Jan 09 2022 *)
%o (Sage)
%o def f(n,k): return 2^(n+k-2)*nth_prime(k) + (n%2)
%o def T(n,k):
%o if (k==0 or k==n): return 1
%o elif (k <= n//2): return f(n,k)
%o else: return f(n,n-k)
%o flatten([[T(n,k) for k in (0..n)] for n in (0..12)]) # _G. C. Greubel_, Jan 09 2022
%K nonn,tabl
%O 0,5
%A _Roger L. Bagula_, Feb 24 2009
%E Edited by _G. C. Greubel_, Jan 09 2022