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%I #9 Jan 23 2022 07:27:32
%S 1,1,1,1,1,1,1,2,2,1,1,3,1,3,1,1,3,2,2,3,1,1,3,3,1,3,3,1,1,3,4,2,2,4,
%T 3,1,1,3,5,3,1,3,5,3,1,1,3,5,4,2,2,4,5,3,1,1,3,5,5,3,1,3,5,5,3,1,1,3,
%U 5,6,4,2,2,4,6,5,3,1,1,3,5,7,5,3,1,3,5,7,5,3,1,1,3,5,7,6,4,2,2,4,6,7,5,3,1
%N Triangle T(n, k) = f(n, k) + f(n, n-k) - 1, where f(n, k) = k if k <= floor(n/4), floor(n/2) - k if floor(n/4) < k <= floor(n/2), k - floor(n/2) if floor(n/2) < k <= floor(3*n/4), otherwise n-k, read by rows.
%H G. C. Greubel, <a href="/A157522/b157522.txt">Rows n = 0..50 of the triangle, flattened</a>
%F T(n, k) = f(n, k) + f(n, n-k) - 1, where f(n, k) = k if k <= floor(n/4), floor(n/2) - k if floor(n/4) < k <= floor(n/2), k - floor(n/2) if floor(n/2) < k <= floor(3*n/4), otherwise n-k.
%F From _G. C. Greubel_, Jan 22 2022: (Start)
%F T(n, n-k) = T(n, k).
%F T(2*n, n) = 1.
%F T(2*n+1, n) = A040000(n).
%F Sum_{k=0..n} T(n, k) = A302488(n). (End)
%e Triangle begins as:
%e 1;
%e 1, 1;
%e 1, 1, 1;
%e 1, 2, 2, 1;
%e 1, 3, 1, 3, 1;
%e 1, 3, 2, 2, 3, 1;
%e 1, 3, 3, 1, 3, 3, 1;
%e 1, 3, 4, 2, 2, 4, 3, 1;
%e 1, 3, 5, 3, 1, 3, 5, 3, 1;
%e 1, 3, 5, 4, 2, 2, 4, 5, 3, 1;
%e 1, 3, 5, 5, 3, 1, 3, 5, 5, 3, 1;
%t f[n_, k_]= 1 +If[k<=Floor[n/4], k, If[Floor[n/4]<k<=Floor[n/2], Floor[n/2]-k, If[Floor[n/2]<k<=Floor[3*n/4], k-Floor[n/2], n-k]]];
%t T[n_, k_]:= f[n,k] +f[n,n-k] -1;
%t Table[T[n, k], {n,0,15}, {k,0,n}]//Flatten (* modified by _G. C. Greubel_, Jan 22 2022 *)
%o (Sage)
%o def f(n, k):
%o if (k <= (n//4)): return k+1
%o elif ((n//4) < k <= (n//2)): return (n//2)-k+1
%o elif ((n//2) < k <= (3*n//4)): return k+1-(n//2)
%o else: return n-k+1
%o def T(n,k): return f(n,k) + f(n,n-k) - 1
%o flatten([[T(n,k) for k in (0..n)] for n in (0..15)]) # _G. C. Greubel_, Jan 22 2022
%Y Cf. A157523.
%K nonn,tabl
%O 0,8
%A _Roger L. Bagula_, Mar 02 2009
%E Edited by _N. J. A. Sloane_, Mar 05 2009
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