A307457 Longest path length in the n-Apollonian network.

3, 6, 14, 30, 62, 126, 254, 510, 1022, 2046, 4094, 8190, 16382, 32766, 65534, 131070, 262142, 524286, 1048574, 2097150, 4194302, 8388606, 16777214, 33554430, 67108862, 134217726, 268435454, 536870910, 1073741822, 2147483646, 4294967294, 8589934590

Offset: 1

Author

Eric W. Weisstein, Apr 08 2019

Keywords

• nonn
• easy

Links

• Eric Weisstein's World of Mathematics, Apollonian Network.
• Eric Weisstein's World of Mathematics, Longest Path.
• Index entries for linear recurrences with constant coefficients, signature (3,-2).

Crossrefs

Essentially the same as A000918 shifted, and A095121.

Cf. A307549.

Formula

a(n) = 2^(n+1) - 2 = A000918(n+1) for n > 1. - Andrew Howroyd, Jun 09 2025

Extensions

a(5) onwards from Andrew Howroyd, Jun 09 2025