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Triangle read by rows, based on array described below.
7

%I #8 Apr 07 2023 02:16:37

%S 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,

%T 64,109,110,111,112,115,120,126,128,229,230,231,232,235,240,245,248,

%U 256,481,482,483,484,485,486,490,496,504,512,1003,1004,1005,1008,1010,1014,1015,1016,1017,1020,1024

%N Triangle read by rows, based on array described below.

%H G. C. Greubel, <a href="/A100461/b100461.txt">Rows n = 1..50 of the triangle, flattened</a>

%F 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.

%e Array begins:

%e 1 2 4 8 16 32 ...

%e * 1 2 6 12 30 ...

%e * * 1 4 9 28 ...

%e * * * 3 8 27 ...

%e * * * * 7 26 ...

%e * * * * * 25 ...

%e and triangle begins:

%e 1;

%e 1, 2;

%e 1, 2, 4;

%e 3, 4, 6, 8;

%e 7, 8, 9, 12, 16;

%e 25, 26, 27, 28, 30, 32;

%e 49, 50, 51, 52, 55, 60, 64;

%e 109, 110, 111, 112, 115, 120, 126, 128;

%t t[n_, k_]:= t[n, k]= If[k==1, 2^(n-1), (n-k+1)*Floor[(t[n, k-1] -1)/(n-k+1)]];

%t Table[t[n, n-k+1], {n,15}, {k,n}]//Flatten (* _G. C. Greubel_, Apr 07 2023 *)

%o (Magma)

%o function t(n,k) // t = A100461

%o if k eq 1 then return 2^(n-1);

%o else return (n-k+1)*Floor((t(n,k-1) -1)/(n-k+1));

%o end if;

%o end function;

%o [t(n,n-k+1): k in [1..n], n in [1..12]]; // _G. C. Greubel_, Apr 07 2023

%o (SageMath)

%o def t(n,k): # t = A100461

%o if (k==1): return 2^(n-1)

%o else: return (n-k+1)*((t(n, k-1) -1)//(n-k+1))

%o 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

%Y Cf. A100452, A100462, A119444.

%K nonn,tabl

%O 1,3

%A _N. J. A. Sloane_, Nov 22 2004