A131507 - OEIS

%I #35 Oct 20 2019 10:25:25

%S 1,3,3,5,5,5,7,7,7,7,9,9,9,9,9,11,11,11,11,11,11,13,13,13,13,13,13,13,

%T 15,15,15,15,15,15,15,15,17,17,17,17,17,17,17,17,17,19,19,19,19,19,19,

%U 19,19,19,19,21,21,21,21,21,21,21,21,21,21,21,23,23,23,23,23,23,23,23,23,23,23,23

%N 2n+1 appears n+1 times.

%C Sum of terms of row n is (n+1)*(2n+1) = A000384(n+1). - _Michel Marcus_, Feb 02 2014

%C Where records occur give A000217. - _Omar E. Pol_, Nov 05 2015

%H Reinhard Zumkeller, <a href="/A131507/b131507.txt">Rows n = 0..125 of triangle, flattened</a>

%F a(n) = 2*floor(sqrt(2n+1)+1/2) - 1. - _Ridouane Oudra_, Oct 20 2019

%e As a triangle, the sequence starts:

%e 1;

%e 3, 3;

%e 5, 5, 5;

%e 7, 7, 7, 7;

%e 9, 9, 9, 9, 9;

%e ...

%p seq(2*floor(sqrt(2*n+1)+1/2)-1, n=0..70); # _Ridouane Oudra_, Oct 20 2019

%t Table[2 n + 1, {n, 0, 11}, {n + 1}] // Flatten (* _Michael De Vlieger_, Nov 05 2015 *)

%o (Haskell)

%o a131507 n k = a131507_tabl !! n !! k

%o a131507_row n = a131507_tabl !! n

%o a131507_tabl = zipWith ($) (map replicate [1..]) [1, 3 ..]

%o a131507_list = concat a131507_tabl

%o -- _Reinhard Zumkeller_, Jul 12 2014, Mar 18 2011

%o (Chipmunk BASIC v3.6.4(b8)) # http://www.nicholson.com/rhn/basic/

%o for n=1 to 23 step 2

%o for j=1 to n  step 2

%o print str$(n)+", ";

%o next j : next n : print

%o end

%o # _Jeremy Gardiner_, Feb 02 2014

%Y Cf. A000217, A002024, A003056, A005408.

%Y Cf. A001650.

%K nonn,tabl

%O 0,2

%A _Paul Curtz_, Aug 13 2007