

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
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OFFSET

1,2


COMMENTS

Row sums = A002411: (1, 6, 18, 40, 75, ...).
Central terms: T(2*n1,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*n7))/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 !! (n1) !! (k1)
a127739_row n = a127739_tabl !! (n1)
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



