A304585 A linear mapping a(n) = x + d*n of pairs of nonnegative integers (x,d), where the pairs are enumerated by meandering antidiagonals.

0, 1, 2, 6, 5, 2, 3, 9, 17, 27, 40, 34, 26, 16, 4, 5, 20, 37, 56, 77, 100, 126, 111, 94, 75, 54, 31, 6, 7, 35, 65, 97, 131, 167, 205, 245, 288, 260, 230, 198, 164, 128, 90, 50, 8, 9, 54, 101, 150, 201, 254, 309, 366, 425, 486, 550, 505, 458, 409, 358, 305, 250, 193, 134, 73, 10, 11

Offset: 0

Author

Hugo Pfoertner, May 16 2018

Keywords

• nonn

Comments

The sequence is an alternative solution to the riddle described in the comments of A304584.

Examples

			  d:
  5 |  20
  4 |  10  19
  3 |   9  11  18
  2 |   3   8  12  17
  1 |   2   4   7  13  16
  0 |   0   1   5   6  14  15
    |________________________
  x:    0   1   2   3   4   5
.
a(13)= 3 + 13*1 = 16 because the 13th position in the enumeration corresponds to x=3 and d=1.
		

Links

• Rainer Rosenthal, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A304584, A304586, A304587.

Programs

Maple

pos2pM:=proc(n) local w,k,e;w:=floor(sqrt(2*n));if w*(w+1)>2*n then k:=w-1;else k:=w;fi;e:=n-k*(k+1)/2;if modp(k,2)=1 then return [k-e,e];else return [e,k-e];fi end: WhereFlea:=proc(n) local x,d,pair; pair:=pos2pM(n);x:=pair[1];d:=pair[2];return x+d*n;end: seq(WhereFlea(n),n=0..66); # Rainer Rosenthal, May 23 2018