A227221 Volume of Johnson square pyramid placed upright on cube (rounded down) with edge lengths equal to n.

1, 9, 33, 79, 154, 266, 423, 632, 900, 1235, 1644, 2135, 2714, 3390, 4170, 5061, 6071, 7206, 8475, 9885, 11443, 13157, 15034, 17082, 19307, 21718, 24322, 27126, 30137, 33363, 36812, 40491, 44407, 48568, 52980, 57652, 62592, 67805, 73300, 79084, 85165, 91550, 98246

Offset

1,2

Comments

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.

Links

K. D. Bajpai, Table of n, a(n) for n = 1..1000

Wikipedia, Square pyramid

Example

a(4) = 79: volume = sqrt(2)/6*k^3 + k^3 = sqrt(2)/6*4^3 + 4^3 = 79.0849446... and floor(79.0849446...) = 79.

Maple

KD:= proc() local a, b; a:=evalf(sqrt(2))/6*k^3 + k^3; b:=floor(a);   RETURN(b):  end: seq(KD(), k=1..100);

Crossrefs

Cf. A224837.

Sequence in context: A103602 A205796 A081585 * A273316 A101990 A147170

Adjacent sequences: A227218 A227219 A227220 * A227222 A227223 A227224

Keyword

nonn

Author

K. D. Bajpai, Sep 19 2013

Status

approved