A055087 - OEIS

%I #21 Nov 24 2024 01:53:21

%S 0,0,0,1,0,1,0,1,2,0,1,2,0,1,2,3,0,1,2,3,0,1,2,3,4,0,1,2,3,4,0,1,2,3,

%T 4,5,0,1,2,3,4,5,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,7,0,1,2,3,

%U 4,5,6,7,0,1,2,3,4,5,6,7,8,0,1,2,3,4,5,6,7,8,0,1,2,3,4,5,6,7,8,9,0,1

%N Integers 0..n then 0..n then 0..n+1 then 0..n+1 etc.

%C Second column in the monotonic justified array of all positive generalized Fibonacci sequences (A160271). see also A199474. - _Casey Mongoven_, Nov 06 2011

%C Can also be seen as an irregular triangle with duplicated rows of A002262. - _Reinhard Zumkeller_, Jul 14 2015

%H Reinhard Zumkeller, <a href="/A055087/b055087.txt">Rows n = 0..120 of triangle, flattened</a>

%H Michael Somos, <a href="/A073189/a073189.txt">Sequences used for indexing triangular or square arrays</a>

%e 0; 0; 0,1; 0,1; 0,1,2; 0,1,2; 0,1,2,3; 0,1,2,3; ...

%t With[{nn=10},Flatten[Table[{Range[0,n],Range[0,n]},{n,0,nn}]]] (* _Harvey P. Dale_, May 30 2015 *)

%o (PARI) {a(n) = (1 + 4*n - sqr( floor( sqrt( 1 + 4*n)))) \ 4}

%o (Haskell)

%o import Data.List (transpose)

%o a055087 n k = a055087_tabf !! n !! k

%o a055087_row n = a055087_tabf !! n

%o a055087_tabf = concat $ transpose [a002262_tabl, a002262_tabl]

%o a055087_list = concat a055087_tabf

%o -- _Reinhard Zumkeller_, Jul 14 2015

%Y  Cf. A002262.

%K nonn,easy,tabf

%O 0,9

%A _Michael Somos_, Jun 13 2000