A085349 Ratio-determined insertion sequence I(0.26688) (see the link below).

1, 4, 15, 71, 269, 1274, 4827, 22861, 86617, 410224, 1554279, 7361171, 27890405, 132090854, 500473011, 2370274201, 8980623793, 42532844764, 161150755263, 763220931551, 2891732970941, 13695443923154, 51890042721675

Offset: 1

Author

John W. Layman, Jun 24 2003

Keywords

• nonn

Comments

This is one of the "twin" ratio-determined insertion sequences (RDIS) that are "children" in the next generation below the "parent" sequences I(0.25024) (A004253) and I(0.26816) (A001353) in the recurrence tree of RDIS sequences. The RDIS twin of this sequence is A085348. See the link for an explanation of RDIS twin. See A082630 or A082981 for other recent examples of RDIS sequences.

Links

• John W. Layman, Ratio-Determined Insertion Sequences and the Tree of their Recurrence Types, June 2003 [Broken link]
• John W. Layman, Ratio-Determined Insertion Sequences and the Tree of their Recurrence Types, June 2003 [local copy, corrected]
• John W. Layman, Sequences Generated by Age-Determined Insertion Trees, Jan 2006
• John W. Layman, Sequences Generated by Age-Determined Insertion Trees, Jan 2006 [Local copy]
• Index entries for linear recurrences with constant coefficients, signature (0, 18, 0, -1).

Crossrefs

Cf. A001353, A004253, A082630, A082981, A085348.

Programs

Mathematica

LinearRecurrence[{0,18,0,-1},{1,4,15,71},30] (* Harvey P. Dale, Mar 04 2013 *)

Formula

It appears that a(n)=18a(n-2)-a(n-4).

Apparently a(n)a(n+3) = 11 + a(n+1)a(n+2). - Ralf Stephan, May 29 2004