A186390 Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) after g(j) when f(i)=g(j), where f(i)=6i and g(j)=j(j+1)/2 (triangular number). Complement of A186389.

1, 2, 3, 5, 7, 9, 11, 13, 16, 19, 21, 24, 28, 31, 34, 38, 42, 46, 50, 54, 59, 64, 68, 73, 79, 84, 89, 95, 101, 107, 113, 119, 126, 133, 139, 146, 154, 161, 168, 176, 184, 192, 200, 208, 217, 226, 234, 243, 253, 262, 271, 281, 291, 301, 311, 321, 332, 343, 353, 364, 376, 387, 398, 410, 422, 434, 446, 458, 471, 484, 496, 509, 523, 536, 549, 563, 577, 591, 605, 619, 634, 649, 663, 678, 694, 709

Offset

1,2

Links

Table of n, a(n) for n=1..86.

Formula

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

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

G.f.: x*(x^6 - x^2 - 1)/((x - 1)^3*(x^2 + 1)*(x^2 + x + 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 after the triangular:
a=(4,6,8,10,12,14,15,17,...)=A186389
b=(1,2,3,5,7,9,11,13,16,...)=A186390.

Mathematica

(* See A186389 *)

Crossrefs

Cf. A186387, A186388, A185390.

Sequence in context: A096149 A033055 A287374 * A022554 A097046 A248420

Adjacent sequences: A186387 A186388 A186389 * A186391 A186392 A186393

Keyword

nonn

Author

Clark Kimberling, Feb 19 2011

Status

approved