%I #25 Jan 10 2024 23:58:40
%S 1,2,2,3,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,
%T 7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,
%U 9,9,9,9,9,10,10,10,10,10,10,10,10,10,10,10,10,10
%N a(n) = floor(3/2 + sqrt(n)).
%C Burning number of the n-ladder (for n >= 1), n-Moebius ladder (for n >= 3), and n-prism (for n >= 3) graphs.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/BurningNumber.html">Burning Number</a>.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/LadderGraph.html">Ladder Graph</a>.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MoebiusLadder.html">Moebius Ladder</a>.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PrismGraph.html">Prism Graph</a>.
%F a(n) = A000194(n) + 1. - _Andrew Howroyd_, Jan 10 2024
%F G.f.: x*(1 + QPochhammer(-x^2, x^4)*QPochhammer(x^8, x^8))/(1 - x).
%t Table[Floor[3/2 + Sqrt[n]], {n, 50}]
%t Floor[3/2 + Sqrt[Range[50]]]
%t CoefficientList[Series[(1 + QPochhammer[-x^2, x^4] QPochhammer[x^8, x^8])/(1 - x), {x, 0, 50}], x]
%Y Sequence agrees with the known terms of A155934.
%Y Cf. A000194, A003059.
%K nonn,easy
%O 0,2
%A _Eric W. Weisstein_, Jan 10 2024
%E Terms a(26) and beyond from _Andrew Howroyd_, Jan 10 2024