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
KEYWORD
nonn,tabl
AUTHOR
N. J. A. Sloane, Nov 22 2004
STATUS
approved