A100461 Triangle read by rows, based on array described below.

1, 1, 2, 1, 2, 4, 3, 4, 6, 8, 7, 8, 9, 12, 16, 25, 26, 27, 28, 30, 32, 49, 50, 51, 52, 55, 60, 64, 109, 110, 111, 112, 115, 120, 126, 128, 229, 230, 231, 232, 235, 240, 245, 248, 256, 481, 482, 483, 484, 485, 486, 490, 496, 504, 512, 1003, 1004, 1005, 1008, 1010, 1014, 1015, 1016, 1017, 1020, 1024

Offset: 1

Author

N. J. A. Sloane, Nov 22 2004

Keywords

• nonn
• tabl

Examples

			Array begins:
  1  2  4  8  16  32 ...
  *  1  2  6  12  30 ...
  *  *  1  4   9  28 ...
  *  *  *  3   8  27 ...
  *  *  *  *   7  26 ...
  *  *  *  *   *  25 ...
and triangle begins:
    1;
    1,   2;
    1,   2,   4;
    3,   4,   6,   8;
    7,   8,   9,  12,  16;
   25,  26,  27,  28,  30,  32;
   49,  50,  51,  52,  55,  60,  64;
  109, 110, 111, 112, 115, 120, 126, 128;
		

Links

• G. C. Greubel, Rows n = 1..50 of the triangle, flattened

Crossrefs

Cf. A100452, A100462, A119444.

Programs

Magma

function t(n,k) // t = A100461
  if k eq 1 then return 2^(n-1);
  else return (n-k+1)*Floor((t(n,k-1) -1)/(n-k+1));
  end if;
end function;
[t(n,n-k+1): k in [1..n], n in [1..12]]; // G. C. Greubel, Apr 07 2023

Mathematica

t[n_, k_]:= t[n, k]= If[k==1, 2^(n-1), (n-k+1)*Floor[(t[n, k-1] -1)/(n-k+1)]];
Table[t[n, n-k+1], {n,15}, {k,n}]//Flatten (* G. C. Greubel, Apr 07 2023 *)

SageMath

def t(n,k): # t = A100461
    if (k==1): return 2^(n-1)
    else: return (n-k+1)*((t(n, k-1) -1)//(n-k+1))
flatten([[t(n,n-k+1) for k in range(1,n+1)] for n in range(1,16)]) # G. C. Greubel, Apr 07 2023

Formula

Form an array t(m,n) (n >= 1, 1 <= m <= n) by: t(1,n) = 2^(n-1) for all n; t(m+1,n) = (n-m)*floor( (t(m,n) - 1)/(n-m) ) for 1 <= m <= n-1.