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, 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

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