A085376 Ratio-dependent insertion sequence I(0.36704) (see the link below).

1, 3, 11, 30, 109, 297, 1079, 2940, 10681, 29103, 105731, 288090, 1046629, 2851797, 10360559, 28229880, 102558961, 279447003, 1015229051, 2766240150, 10049731549, 27382954497, 99482086439, 271063304820, 984771132841

Offset: 1

Author

John W. Layman, Jun 26 2003

Keywords

• nonn

Comments

This sequence is the ratio-determined insertion sequence (RDIS) "twin" of I(0.37802)=A080874 and "child" of I(0.33344)=A001835 and I(0.38208)=A001906 in the RDIS recurrence tree (see the link for an explanation of terms). See A082630, A082981, A085348 and A085349 for recent examples of RDIS sequences.

Conjecture: partial sums of A129445. - Sean A. Irvine, Jul 14 2022

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]

Crossrefs

Cf. A001835, A001906, A080874, A082630, A082981, A085348, A085349.

Formula

It is conjectured that a(n) = 10*a(n-2) - a(n-4).

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