A368941 a(n) = floor(3/2 + sqrt(n)).

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, 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, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10

Offset: 0

Author

Eric W. Weisstein, Jan 10 2024

Keywords

• nonn
• easy

Comments

Burning number of the n-ladder (for n >= 1), n-Moebius ladder (for n >= 3), and n-prism (for n >= 3) graphs.

Links

• Eric Weisstein's World of Mathematics, Burning Number.
• Eric Weisstein's World of Mathematics, Ladder Graph.
• Eric Weisstein's World of Mathematics, Moebius Ladder.
• Eric Weisstein's World of Mathematics, Prism Graph.

Crossrefs

Sequence agrees with the known terms of A155934.

Cf. A000194, A003059.

Programs

Mathematica

Table[Floor[3/2 + Sqrt[n]], {n, 50}]
Floor[3/2 + Sqrt[Range[50]]]
CoefficientList[Series[(1 + QPochhammer[-x^2, x^4]  QPochhammer[x^8, x^8])/(1 - x), {x, 0, 50}], x]

Formula

a(n) = A000194(n) + 1. - Andrew Howroyd, Jan 10 2024

G.f.: x*(1 + QPochhammer(-x^2, x^4)*QPochhammer(x^8, x^8))/(1 - x).

Extensions

Terms a(26) and beyond from Andrew Howroyd, Jan 10 2024