A138036 Write n = C(i,2)+C(j,1) with i>j>=0; let L[n] = [i,j]; sequence gives list of pairs L[n], n >= 0.
1, 0, 2, 0, 2, 1, 3, 0, 3, 1, 3, 2, 4, 0, 4, 1, 4, 2, 4, 3, 5, 0, 5, 1, 5, 2, 5, 3, 5, 4, 6, 0, 6, 1, 6, 2, 6, 3, 6, 4, 6, 5, 7, 0, 7, 1, 7, 2, 7, 3, 7, 4, 7, 5, 7, 6, 8, 0, 8, 1, 8, 2, 8, 3, 8, 4, 8, 5, 8, 6, 8, 7, 9, 0, 9, 1, 9, 2, 9, 3, 9, 4, 9, 5, 9, 6, 9, 7, 9, 8, 10, 0, 10, 1, 10, 2, 10, 3, 10, 4, 10, 5, 10, 6, 10, 7, 10, 8, 10, 9, 11, 0, 11, 1, 11, 2, 11, 3, 11, 4
Offset: 0
Examples
The pairs L[0] through L[10] are [1, 0] [2, 0] [2, 1] [3, 0] [3, 1] [3, 2] [4, 0] [4, 1] [4, 2] [4, 3] [5, 0]
References
- D. E. Knuth, The Art of Computer Programming, vol. 4A, Combinatorial Algorithms, Section 7.2.1.3, Eq. (20), p. 360.
Programs
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Mathematica
A138036list[len_] := Module[{i = 0, j = 1, L = {1, 0}}, Do[i++; If[i == j, j++; i = 0]; AppendTo[L, j]; AppendTo[L, i], {len}]; L]; A138036list[60] (* Jean-François Alcover, Jul 11 2019, after Peter Luschny *)
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Sage
def A138036_list(len): i, j = 0, 1 L = [1, 0] for _ in range(len): i += 1 if i == j: j += 1 i = 0 L.append(j) L.append(i) return L A138036_list(47) # Peter Luschny, May 18 2015
Comments