A229063 Volume of the Johnson square pyramid (rounded down) with all the edge lengths equal to n.

0, 1, 6, 15, 29, 50, 80, 120, 171, 235, 313, 407, 517, 646, 795, 965, 1158, 1374, 1616, 1885, 2182, 2509, 2867, 3258, 3682, 4142, 4639, 5174, 5748, 6363, 7021, 7723, 8470, 9264, 10105, 10996, 11939, 12933, 13981, 15084, 16244, 17462, 18739, 20078, 21478, 22942

Offset: 1

Author

K. D. Bajpai, Sep 17 2013

Keywords

• nonn

Comments

Johnson square pyramid: Square base with four equilateral triangular-faces. All the edge lengths are equal to n.

Examples

			a(9)=171:  Volume= sqrt(2)/6*n^3= sqrt(2)/6*9^3= 171.8269478 and floor(171.8269478)= 171.
		

Links

• K. D. Bajpai, Table of n, a(n) for n = 1..1000
• Wikipedia, Square pyramid

Crossrefs

Cf. A228189.

Programs

Maple

A229063 := proc(n)
    floor(n^3*sqrt(2)/6) ;
end proc:

Mathematica

Table[Floor[k^3*Sqrt[2]/6],{k,1,100}]

Formula

a(n) = floor(n^3*sqrt(2)/6)