A227221 - OEIS

%I #21 Sep 26 2024 17:10:38

%S 1,9,33,79,154,266,423,632,900,1235,1644,2135,2714,3390,4170,5061,

%T 6071,7206,8475,9885,11443,13157,15034,17082,19307,21718,24322,27126,

%U 30137,33363,36812,40491,44407,48568,52980,57652,62592,67805,73300,79084,85165,91550,98246

%N Volume of Johnson square pyramid placed upright on cube (rounded down) with edge lengths equal to n.

%C Johnson square pyramid: a square base with four equilateral triangle- faces. It is placed upright on top of the cube. All the edge lengths are equal.

%H Georg Fischer, <a href="/A227221/b227221.txt">Table of n, a(n) for n = 1..1000</a> [first 203 terms from _K. D. Bajpai_]

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Square_pyramid">Square pyramid</a>

%e a(4) = 79: volume = sqrt(2)/6*k^3 + k^3 = sqrt(2)/6*4^3 + 4^3 = 79.0849... and floor(79.0849...) = 79.

%p a:= n-> floor((sqrt(2)/6 + 1)*n^3):

%p seq(a(n), n=1..43);

%Y Cf. A224837.

%K nonn

%O 1,2

%A _K. D. Bajpai_, Sep 19 2013