A172279 - OEIS

%I #18 Oct 12 2024 02:27:42

%S 1,1,1,1,2,1,1,3,2,1,1,2,6,2,1,1,3,10,5,1,1,1,2,8,20,8,2,1,1,2,11,35,

%T 18,5,1,1,1,1,6,28,70,28,6,1,1,1,1,8,42,126,63,17,4,1,1,1,1,5,24,105,

%U 252,105,24,5,1,1,1,1,6,33,165,462,231,66,17,4,1,1,1,1,4,22,99,396,924,396,99,22,4,1,1

%N Triangle, read by rows: T(n, k) = ceiling( binomial(n, k)/(1 + (k - floor(n/2))^2) ).

%H G. C. Greubel, <a href="/A172279/b172279.txt">Rows n = 0..100 of triangle, flattened</a>

%F T(n, k) = ceiling( binomial(n, k)/(1 + (k - floor(n/2))^2) ).

%F T(2*n, n) = binomial(2*n,n)  (cf. A000984). - _Michel Marcus_, May 22 2019

%e Triangle begins as:

%e   1;

%e   1, 1;

%e   1, 2,  1;

%e   1, 3,  2,  1;

%e   1, 2,  6,  2,   1;

%e   1, 3, 10,  5,   1,   1;

%e   1, 2,  8, 20,   8,   2,   1;

%e   1, 2, 11, 35,  18,   5,   1,  1;

%e   1, 1,  6, 28,  70,  28,   6,  1, 1;

%e   1, 1,  8, 42, 126,  63,  17,  4, 1, 1;

%e   1, 1,  5, 24, 105, 252, 105, 24, 5, 1, 1;

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

%t Table[T[n, k], {n, 0, 12}, {k, 0, n}]//Flatten

%o (PARI)

%o {T(n, k) = ceil(binomial(n, k)/(1 + (k -floor(n/2))^2))};

%o for(n=0, 12, for(k=0,n, print1(T(n,k), ", "))) \\ _G. C. Greubel_, May 21 2019

%o (Magma)

%o T:= func< n,k | Ceiling(Binomial(n, k)/(1 + (k - Floor(n/2))^2)) >;

%o [[T(n,k) : k in [0..n]]: n in [0..12]]; // _G. C. Greubel_, May 21 2019

%o (Sage)

%o def T(n, k): return ceil(binomial(n, k)/(1 + (k -floor(n/2))^2))

%o [[T(n, k) for k in (0..n)] for n in (0..12)] # _G. C. Greubel_, May 21 2019

%Y Cf. A000984 (central binomial coefficients).

%K nonn,tabl

%O 0,5

%A _Roger L. Bagula_, Jan 30 2010

%E Edited by _G. C. Greubel_, May 21 2019