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A127739 Triangle read by rows, in which row n contains the triangular number T(n) = A000217(n) repeated n times. 3

%I

%S 1,3,3,6,6,6,10,10,10,10,15,15,15,15,15,21,21,21,21,21,21,28,28,28,28,

%T 28,28,28,36,36,36,36,36,36,36,36,45,45,45,45,45,45,45,45,45,55,55,55,

%U 55,55,55,55,55,55,55,66,66,66,66,66,66,66,66,66,66,66,78

%N Triangle read by rows, in which row n contains the triangular number T(n) = A000217(n) repeated n times.

%C Row sums = A002411: (1, 6, 18, 40, 75, ...).

%C Central terms: T(2*n-1,n) = A000384(n). - _Reinhard Zumkeller_, Mar 18 2011

%H Reinhard Zumkeller, <a href="/A127739/b127739.txt">Rows n=1..100 of triangle, flattened</a>

%H Boris Putievskiy, <a href="http://arxiv.org/abs/1212.2732">Transformations [of] Integer Sequences And Pairing Functions</a> arXiv:1212.2732 [math.CO]

%F a(n) = A003057(n)*A002024(n)/2; a(n) = (t+2)*(t+1)/2, where t=floor((-1+sqrt(8*n-7))/2). - _Boris Putievskiy_, Feb 08 2013

%e First few rows of the triangle are:

%e 1;

%e 3, 3;

%e 6, 6, 6;

%e 10, 10, 10, 10;

%e 15, 15, 15, 15, 15;

%e ...

%t Table[n(n+1)/2,{n,100},{n}]//Flatten (* _Zak Seidov_, Mar 19 2011 *)

%o (Haskell)

%o a127739 n k = a127739_tabl !! (n-1) !! (k-1)

%o a127739_row n = a127739_tabl !! (n-1)

%o a127739_tabl = zipWith ($) (map replicate [1..]) $ tail a000217_list

%o -- _Reinhard Zumkeller_, Feb 03 2012, Mar 18 2011

%o (PARI) A127739=n->binomial((sqrtint(8*n)+3)\2,2) \\ _M. F. Hasler_, Mar 09 2014

%Y Cf. A000217, A002024, A002411, A003057, A057944.

%K nonn,tabl

%O 1,2

%A _Gary W. Adamson_, Jan 27 2007

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Last modified April 23 08:47 EDT 2019. Contains 322381 sequences. (Running on oeis4.)