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
Examples
1 3 2 3 4 5 7 6 5 4 5 6 7 8 9 11 10 9 8 7 6 ...
Programs
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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
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
Extensions
More terms from Emeric Deutsch, Jan 26 2006