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

%I A304585 #18 Nov 09 2018 18:30:49
%S A304585 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,
%T A304585 54,31,6,7,35,65,97,131,167,205,245,288,260,230,198,164,128,90,50,8,9,
%U A304585 54,101,150,201,254,309,366,425,486,550,505,458,409,358,305,250,193,134,73,10,11
%N A304585 A linear mapping a(n) = x + d*n of pairs of nonnegative integers (x,d), where the pairs are enumerated by meandering antidiagonals.
%C A304585 The sequence is an alternative solution to the riddle described in the comments of A304584.
%H A304585 Rainer Rosenthal, <a href="/A304585/b304585.txt">Table of n, a(n) for n = 0..10000</a>
%e A304585   d:
%e A304585   5 |  20
%e A304585   4 |  10  19
%e A304585   3 |   9  11  18
%e A304585   2 |   3   8  12  17
%e A304585   1 |   2   4   7  13  16
%e A304585   0 |   0   1   5   6  14  15
%e A304585     |________________________
%e A304585   x:    0   1   2   3   4   5
%e A304585 .
%e A304585 a(13)= 3 + 13*1 = 16 because the 13th position in the enumeration corresponds to x=3 and d=1.
%p A304585 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
%Y A304585 Cf. A304584, A304586, A304587.
%K A304585 nonn
%O A304585 0,3
%A A304585 _Hugo Pfoertner_, May 16 2018