A114751 The following triangle contains n consecutive numbers beginning from n in ascending order if n is odd else in descending order. Sequence contains the triangle 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

Table of n, a(n) for n=1..78.

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

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

Status

approved