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

1,3

Links

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

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.

Example

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;

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 *)

Prog

(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
(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

Crossrefs

Cf. A100452, A100462, A119444.

Sequence in context: A302982 A238577 A131380 * A302655 A316997 A323465

Adjacent sequences: A100458 A100459 A100460 * A100462 A100463 A100464

Keyword

nonn,tabl

Author

N. J. A. Sloane, Nov 22 2004

Status

approved