A186388 Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) before g(j) when f(i)=g(j), where f(i)=6i and g(j)=j(j+1)/2 (triangular number). Complement of A186387.

1, 2, 4, 5, 7, 9, 11, 14, 16, 19, 22, 25, 28, 31, 35, 38, 42, 46, 50, 55, 59, 64, 69, 74, 79, 84, 90, 95, 101, 107, 113, 120, 126, 133, 140, 147, 154, 161, 169, 176, 184, 192, 200, 209, 217, 226, 235, 244, 253, 262, 272, 281, 291, 301, 311, 322, 332, 343, 354, 365, 376, 387, 399, 410, 422, 434, 446, 459, 471, 484, 497, 510, 523, 536, 550, 563, 577, 591, 605, 620, 634, 649, 664, 679, 694, 709, 725, 740, 756, 772, 788, 805, 821

Offset

1,2

Links

Table of n, a(n) for n=1..93.

Formula

Conjectures from Chai Wah Wu, May 12 2026: (Start)

a(n) = 2*a(n-1) - a(n-2) + a(n-3) - 2*a(n-4) + a(n-5) - a(n-6) + 2*a(n-7) - a(n-8) + a(n-9) - 2*a(n-10) + a(n-11) for n > 11.

G.f.: x*(x^9 - 2*x^6 + x^5 - x^4 + 2*x^3 - x^2 - 1)/((x - 1)^3*(x^2 + 1)*(x^2 + x + 1)*(x^4 - x^2 + 1)). (End)

Example

First, write
......6.....12..18....24..30. (6i)
1..3..6..10...15....21..28... (triangular)
Then replace each number by its rank, where ties are settled by ranking 6i before the triangular:
a=(3,6,8,10,12,13,15,17,...)=A186387
b=(1,2,4,5,7,9,11,14,16,...)=A186388.

Mathematica

(* See A186387 *)

Crossrefs

Cf. A186350, A186387, A186389, A186390.

Sequence in context: A057352 A156625 A259280 * A058577 A356075 A071917

Adjacent sequences: A186385 A186386 A186387 * A186389 A186390 A186391

Keyword

nonn

Author

Clark Kimberling, Feb 19 2011

Status

approved