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

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, 29, 28, 27, 26, 36, 35, 34, 33, 32, 31, 42, 41, 40, 39, 38, 37, 49, 48, 47, 46, 45, 44, 43, 56, 55, 54, 53, 52, 51, 50, 64, 63, 62, 61, 60, 59, 58, 57

Offset

1,2

Comments

A permutation of the natural numbers. Mentioned as d(n) in A269837.

Difference table:

1, 2, 4, 3, 6, 5, 9, 8, 7, 12, 11, 10, 16, 15, 14, 13, 20, 19, 18, ...

1, 2, -1, 3, -1, 4, -1, -1, 5, -1, -1, 6, -1, -1, -1, 7, -1, -1, -1, ...

1, -3, 4, -4, 5, -5, 0, 6, -6, 0, 7, -7, 0, 0, 8, -8, 0, 0, 9, ...

etc.

Links

Table of n, a(n) for n=1..64.

Formula

With offset=0, a(n) = A271584(n) + A269837(n)

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

Example

Irregular triangle:
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, 29, 28, 27, 26,
etc.

Maple

count:= 0:
for r from 1 to 20 do
  d:= ceil(r/2);
  for i from 0 to d-1 do A[r, i]:= count+ d-i od;
  count:= count+d;
od:
seq(seq(A[r, i], i=0..ceil(r/2)-1), r=1..20); # Robert Israel, Apr 11 2016

Mathematica

Table[Reverse@ Range[Floor[n/2]] + Floor[(n - 1)^2/4], {n, 16}] // Flatten (* Michael De Vlieger, Apr 11 2016 *)

Crossrefs

Cf. A000027, A002620, A024206, A033638, A075356, A235355, A269837, A271584

Sequence in context: A129767 A119618 A113321 * A232643 A366263 A231334

Adjacent sequences: A271644 A271645 A271646 * A271648 A271649 A271650

Keyword

nonn,tabf

Author

Paul Curtz, Apr 11 2016

Status

approved