A157192 - OEIS

%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