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 A157192 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. 1
 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, 1, 1, 129, 385, 1281, 1281, 385, 129, 1, 1, 256, 768, 2560, 7168, 2560, 768, 256, 1, 1, 513, 1537, 5121, 14337, 14337, 5121, 1537, 513, 1, 1, 1024, 3072, 10240, 28672, 90112, 28672, 10240, 3072, 1024, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 LINKS G. C. Greubel, Rows n = 0..50 of the triangle, flattened FORMULA 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. T(n, n-k) = T(n, k). EXAMPLE Triangle begins as: 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, 1; 1, 129, 385, 1281, 1281, 385, 129, 1; 1, 256, 768, 2560, 7168, 2560, 768, 256, 1; 1, 513, 1537, 5121, 14337, 14337, 5121, 1537, 513, 1; 1, 1024, 3072, 10240, 28672, 90112, 28672, 10240, 3072, 1024, 1; MATHEMATICA f[n_, k_]:= Prime[k]*2^(n+k-2) + Mod[n, 2]; T[n_, k_]:= If[k==0 || k==n, 1, If[k<=Floor[n/2], f[n, k], f[n, n-k] ]]; Table[T[n, k], {n, 0, 10}, {k, 0, n}]//Flatten (* modified by G. C. Greubel, Jan 09 2022 *) PROG (Sage) def f(n, k): return 2^(n+k-2)*nth_prime(k) + (n%2) def T(n, k): if (k==0 or k==n): return 1 elif (k <= n//2): return f(n, k) else: return f(n, n-k) flatten([[T(n, k) for k in (0..n)] for n in (0..12)]) # G. C. Greubel, Jan 09 2022 CROSSREFS Sequence in context: A008459 A259333 A180960 * A154982 A347972 A146767 Adjacent sequences: A157189 A157190 A157191 * A157193 A157194 A157195 KEYWORD nonn,tabl AUTHOR Roger L. Bagula, Feb 24 2009 EXTENSIONS Edited by G. C. Greubel, Jan 09 2022 STATUS approved

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Last modified May 31 11:21 EDT 2023. Contains 363066 sequences. (Running on oeis4.)