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A127739 Triangle read by rows, in which row n contains the triangular number T(n) = A000217(n) repeated n times; smallest triangular number greater than or equal to n. 5
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, 28, 28, 28, 36, 36, 36, 36, 36, 36, 36, 36, 45, 45, 45, 45, 45, 45, 45, 45, 45, 55, 55, 55, 55, 55, 55, 55, 55, 55, 55, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 78 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

Central terms: T(2*n-1,n) = A000384(n). - Reinhard Zumkeller, Mar 18 2011

LINKS

Reinhard Zumkeller, Rows n=1..100 of triangle, flattened

Boris Putievskiy, Transformations [of] Integer Sequences And Pairing Functions arXiv:1212.2732 [math.CO], 2012.

FORMULA

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

EXAMPLE

First few rows of the triangle are:

   1;

   3,  3;

   6,  6,  6;

  10, 10, 10, 10;

  15, 15, 15, 15, 15;

  ...

MATHEMATICA

Table[n(n+1)/2, {n, 100}, {n}]//Flatten (* Zak Seidov, Mar 19 2011 *)

PROG

(Haskell)

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

a127739_row n = a127739_tabl !! (n-1)

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

-- Reinhard Zumkeller, Feb 03 2012, Mar 18 2011

(PARI) A127739=n->binomial((sqrtint(8*n)+3)\2, 2) \\ M. F. Hasler, Mar 09 2014

CROSSREFS

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

Sequence in context: A262871 A160745 A105676 * A327142 A175394 A070318

Adjacent sequences:  A127736 A127737 A127738 * A127740 A127741 A127742

KEYWORD

nonn,tabl

AUTHOR

Gary W. Adamson, Jan 27 2007

EXTENSIONS

Name edited by Michel Marcus, Apr 30 2020

STATUS

approved

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Last modified December 8 20:37 EST 2021. Contains 349596 sequences. (Running on oeis4.)