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

0,3

Comments

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

Links

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

Example

  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.

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

Crossrefs

Cf. A304584, A304586, A304587.

Sequence in context: A175995 A271533 A335995 * A336074 A021381 A323501

Adjacent sequences: A304582 A304583 A304584 * A304586 A304587 A304588

Keyword

nonn

Author

Hugo Pfoertner, May 16 2018

Status

approved