A368942 Burning number of the n-antiprism graph.

2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10

Offset: 1

Author

Eric W. Weisstein, Jan 10 2024

Keywords

• nonn

Comments

The n-antiprism graph is defined for n >= 3. The sequence has been extended to n=1 using the formula. - Andrew Howroyd, Jan 10 2024

Links

• Eric Weisstein's World of Mathematics, Antiprism Graph.
• Eric Weisstein's World of Mathematics, Burning Number.

Crossrefs

Cf. A156859, A204166, A351846.

Programs

Mathematica

Table[Floor[(Sqrt[16 n - 1] + 5)/4], {n, 50}]
Floor[(Sqrt[16 Range[50] - 1] + 5)/4]

PARI

a(n) = {1 + (sqrtint(16*n - 1) + 1)\4} \\ Andrew Howroyd, Jan 10 2024

Formula

a(n) = A204166(2*n) = A351846(2*n-1) + 1 = floor((sqrt(16*n - 1) + 1)/4) + 1. - Andrew Howroyd, Jan 10 2024

Extensions

a(1)-a(2) and terms a(34) and beyond from Andrew Howroyd, Jan 10 2024