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 A214859 Triangle read by rows, T(n,k) = n^2 - k*(k+1)/2 if k*(k+1)/2 <= n^2. 0

%I

%S 0,1,0,4,3,1,9,8,6,3,16,15,13,10,6,1,25,24,22,19,15,10,4,36,35,33,30,

%T 26,21,15,8,0,49,48,46,43,39,34,28,21,13,4,64,63,61,58,54,49,43,36,28,

%U 19,9,81,80,78,75,71,66,60,53,45,36,26,15,3,100,99,97

%N Triangle read by rows, T(n,k) = n^2 - k*(k+1)/2 if k*(k+1)/2 <= n^2.

%C Row lengths are in A214857.

%F T(2*n,n) = A022264(n).

%F T(n,n) = n*(n-1)/2 = A000217(n-1).

%e Triangle begins

%e 0

%e 1, 0

%e 4, 3, 1

%e 9, 8, 6, 3

%e 16, 15, 13, 10, 6, 1

%e 25, 24, 22, 19, 15, 10, 4

%e 36, 35, 33, 30, 26, 21, 15, 8, 0

%e 49, 48, 46, 43, 39, 34, 28, 21, 13, 4

%e 64, 63, 61, 58, 54, 49, 43, 36, 28, 19, 9

%e 81, 80, 78, 75, 71, 66, 60, 53, 45, 36, 26, 15, 3

%e 100, 99, 97, 94, 90, 85, 79, 72, 64, 55, 45, 34, 22, 9

%e 121, 120, 118, 115, 111, 106, 100, 93, 85, 76, 66, 55, 43, 30, 16, 1

%e ...

%t Table[s = {}; k = 0; While[tri = k*(k + 1)/2; tri <= n^2, AppendTo[s, n^2 - tri]; k++]; s, {n, 0, 10}] (* _T. D. Noe_, Mar 11 2013 *)

%Y Cf. Diagonals: A000217, A034856, A055999,

%Y Columns: A000290, A005563, A028872, A028878,

%K nonn,easy,tabf

%O 0,4

%A _Philippe DelĂ©ham_, Mar 09 2013

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Last modified August 10 07:37 EDT 2020. Contains 336368 sequences. (Running on oeis4.)