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Irregular triangle T(n,k) read by rows: n repetitions of -1 followed by (n+1) repetitions of n+1.
0

%I #8 May 07 2014 16:45:30

%S 1,-1,2,2,-1,-1,3,3,3,-1,-1,-1,4,4,4,4,-1,-1,-1,-1,5,5,5,5,5,-1,-1,-1,

%T -1,-1,6,6,6,6,6,6,-1,-1,-1,-1,-1,-1,7,7,7,7,7,7,7,-1,-1,-1,-1,-1,-1,

%U -1,8,8,8,8,8,8,8,8,-1,-1,-1,-1,-1,-1,-1,-1,9,9,9,9,9,9,9,9,9,-1,-1,-1,-1,-1,-1,-1,-1,-1,10,10,10,10,10,10,10,10,10,10

%N Irregular triangle T(n,k) read by rows: n repetitions of -1 followed by (n+1) repetitions of n+1.

%C Row n has 2n+1 terms.

%e 1,

%e -1, 2, 2,

%e -1, -1, 3, 3, 3,

%e -1, -1, -1, 4, 4, 4, 4,

%e -1, -1, -1, -1, 5, 5, 5, 5, 5,

%e -1, -1, -1, -1, -1, 6, 6, 6, 6, 6, 6,

%e -1, -1, -1, -1, -1, -1, 7, 7, 7, 7, 7, 7, 7,

%e -1, -1, -1, -1, -1, -1, -1, 8, 8, 8, 8, 8, 8, 8, 8,

%e -1, -1, -1, -1, -1, -1, -1, -1, 9, 9, 9, 9, 9, 9, 9, 9, 9,

%e -1, -1, -1, -1, -1, -1, -1, -1, -1, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10

%t Flatten[Table[Join[PadRight[{},n,-1],PadRight[{},n+1,n+1]],{n,0,9}]] (* _Harvey P. Dale_, May 07 2014 *)

%Y Cf. A002061 (row sums).

%K sign,tabf,easy

%O 0,3

%A _Paul Curtz_, Jun 16 2008