1,1

The n-flower graph can be defined without using parallel edges for n >= 3. It is a snark for odd n >= 5. The sequence has been extended to n=1 using the recurrence. - Andrew Howroyd, May 24 2025

Andrew Howroyd, Table of n, a(n) for n = 1..200

Eric Weisstein's World of Mathematics, Flower Graph.

Eric Weisstein's World of Mathematics, Vertex-Induced Subgraph.

Index entries for linear recurrences with constant coefficients, signature (22,-150,226,1112,-5450,11884,-6878, -44971,146976,-284908,407972, -438909,443802,14624,-1169814,2380928, -2419194,370978,306798,-41711,3516276, -7451820,4641152,6836032,-10088448,-1251200, 4632064,258560,-217088,-462848, -204800,86016,16384,16384).

a(n) = 16^n - A362793(n) - 1.

G.f.: x*(12 - 164*x + 1188*x^2 - 6670*x^3 + 30712*x^4 - 157814*x^5 + 535856*x^6 - 1226534*x^7 + 1551888*x^8 + 4984*x^9 - 4575116*x^10 + 13495862*x^11 - 21808180*x^12 + 20106522*x^13 - 11358320*x^14 + 10928178*x^15 - 30026404*x^16 + 58877492*x^17 - 21768152*x^18 - 120536708*x^19 + 215936116*x^20 - 192382876*x^21 + 129015952*x^22 + 33170240*x^23 - 144954048*x^24 + 31882112*x^25 - 5940992*x^26 + 18928640*x^27 + 3677184*x^28 + 2224128*x^29 - 872448*x^30 - 335872*x^31 + 32768*x^32 + 49152*x^33)/((1 - x)^3*(1 + x)^3*(1 - 5*x + 9*x^2 - 10*x^3 + 4*x^4)^2*(1 + 5*x + 9*x^2 + 10*x^3 + 4*x^4)^2*(1 - 11*x + 23*x^2 - 47*x^3 + 46*x^4 + 4*x^5 + 8*x^6)^2). - Andrew Howroyd, May 24 2025

Cf. A362793 (number of vertex cuts).

Sequence in context: A338811 A199681 A211403 * A008547 A381052 A109020

Adjacent sequences: A362804 A362805 A362806 * A362808 A362809 A362810

nonn,easy

Eric W. Weisstein, May 04 2023

a(1)-a(4) and a(8) onwards from Andrew Howroyd, May 24 2025

approved