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Burning number of the n-antiprism graph.
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%I #15 Feb 16 2025 08:34:06

%S 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,

%T 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,

%U 9,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10

%N Burning number of the n-antiprism graph.

%C 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

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/AntiprismGraph.html">Antiprism Graph</a>.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BurningNumber.html">Burning Number</a>.

%F a(n) = A204166(2*n) = A351846(2*n-1) + 1 = floor((sqrt(16*n - 1) + 1)/4) + 1. - _Andrew Howroyd_, Jan 10 2024

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

%t Floor[(Sqrt[16 Range[50] - 1] + 5)/4]

%o (PARI) a(n) = {1 + (sqrtint(16*n - 1) + 1)\4} \\ _Andrew Howroyd_, Jan 10 2024

%Y Cf. A156859, A204166, A351846.

%K nonn,changed

%O 1,1

%A _Eric W. Weisstein_, Jan 10 2024

%E a(1)-a(2) and terms a(34) and beyond from _Andrew Howroyd_, Jan 10 2024