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A271647 Irregular triangle read by rows: the natural numbers from right to left.

%I A271647 #16 Apr 11 2016 22:17:31
%S A271647 1,2,4,3,6,5,9,8,7,12,11,10,16,15,14,13,20,19,18,17,25,24,23,22,21,30,
%T A271647 29,28,27,26,36,35,34,33,32,31,42,41,40,39,38,37,49,48,47,46,45,44,43,
%U A271647 56,55,54,53,52,51,50,64,63,62,61,60,59,58,57
%N A271647 Irregular triangle read by rows: the natural numbers from right to left.
%C A271647 A permutation of the natural numbers. Mentioned as d(n) in A269837.
%C A271647 Difference table:
%C A271647 1,  2,  4,  3,  6,  5,  9,  8,  7, 12, 11, 10, 16, 15, 14, 13, 20, 19, 18, ...
%C A271647 1,  2, -1,  3, -1,  4, -1, -1,  5, -1, -1,  6, -1, -1, -1,  7, -1, -1, -1, ...
%C A271647 1, -3,  4, -4,  5, -5,  0,  6, -6,  0,  7, -7,  0,  0,  8, -8,  0,  0,  9, ...
%C A271647 etc.
%F A271647 With offset=0, a(n) = A271584(n) + A269837(n)
%F A271647 Empirical g.f. as triangle: (1-y*x^3+y^2*x^4-2*y*x^4-y^2*x^5+y*x^5+y^2*x^7)*x/((1+x)*(1-x)^3*(1-y*x^2)^3). - _Robert Israel_, Apr 11 2016
%e A271647 Irregular triangle:
%e A271647 1,
%e A271647 2,
%e A271647 4,   3,
%e A271647 6,   5,
%e A271647 9,   8,  7,
%e A271647 12, 11, 10,
%e A271647 16, 15, 14, 13,
%e A271647 20, 19, 18, 17,
%e A271647 25, 24, 23, 22, 21,
%e A271647 30, 29, 28, 27, 26,
%e A271647 etc.
%p A271647 count:= 0:
%p A271647 for r from 1 to 20 do
%p A271647   d:= ceil(r/2);
%p A271647   for i from 0 to d-1 do A[r,i]:= count+ d-i od;
%p A271647   count:= count+d;
%p A271647 od:
%p A271647 seq(seq(A[r,i],i=0..ceil(r/2)-1),r=1..20); # _Robert Israel_, Apr 11 2016
%t A271647 Table[Reverse@ Range[Floor[n/2]] + Floor[(n - 1)^2/4], {n, 16}] // Flatten (* _Michael De Vlieger_, Apr 11 2016 *)
%Y A271647 Cf. A000027, A002620, A024206, A033638, A075356, A235355, A269837, A271584
%K A271647 nonn,tabf
%O A271647 1,2
%A A271647 _Paul Curtz_, Apr 11 2016