A114751 Triangle where row n contains the n consecutive numbers from n to 2n-1, in ascending order if n is odd, else in descending order; listed by rows.

1, 3, 2, 3, 4, 5, 7, 6, 5, 4, 5, 6, 7, 8, 9, 11, 10, 9, 8, 7, 6, 7, 8, 9, 10, 11, 12, 13, 15, 14, 13, 12, 11, 10, 9, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12

Offset

1,2

Links

Paolo Xausa, Table of n, a(n) for n = 1..11325 (rows 1..150 of triangle, flattened).

Formula

a(n) = (3*t+2-t*(-1)^(t-1))/2-(1+(-1)^t)*(j-1)/2+(1-(-1)^t)*(j-1)/2, where j = (t*t+3*t+4)/2-n, t=floor((-1+sqrt(8*n-7))/2). - Boris Putievskiy, Jan 30 2013

Example

1
3 2
3 4 5
7 6 5 4
5 6 7 8 9
11 10 9 8 7 6
...

Maple

for n from 1 to 14 do if n mod 2 = 1 then print(seq(k, k=n..2*n-1)) else print(seq(2*n-k, k=1..n)) fi od; # yields sequence in triangular form # Emeric Deutsch, Jan 26 2006

Mathematica

A114751row[n_] := If[OddQ[n], Range[n, 2*n-1], Range[2*n-1, n, -1]];
Array[A114751row, 15] (* Paolo Xausa, Jun 11 2026 *)

Prog

(PARI) A114751_row(n)=if(n%2, [n..n*2-1], -[1-2*n..-n]) \\ M. F. Hasler, Jun 04 2026
A114751(n, k=0)=if(!k, A114751(k=sqrtint(8*n-7)\/2, n-k*(k-1)/2), n%2, n+k-1, 2*n-k) \\ gives either T(n, k) or a(n), if k isn't provided. - M. F. Hasler, Jun 04 2026

Crossrefs

Cf. A114752, A114753, A210530.

Sequence in context: A292787 A335944 A035366 * A211947 A220071 A132408

Adjacent sequences: A114748 A114749 A114750 * A114752 A114753 A114754

Keyword

easy,nonn,tabl

Author

Amarnath Murthy, Nov 15 2005

Extensions

More terms from Emeric Deutsch, Jan 26 2006

Better definition from M. F. Hasler, Jun 13 2026

Status

approved