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A227221
Volume of Johnson square pyramid placed upright on cube (rounded down) with edge lengths equal to n.
1
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
Georg Fischer, Table of n, a(n) for n = 1..1000 [first 203 terms from K. D. Bajpai]
Wikipedia, Square pyramid
EXAMPLE
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.
MAPLE
a:= n-> floor((sqrt(2)/6 + 1)*n^3):
seq(a(n), n=1..43);
CROSSREFS
Cf. A224837.
Sequence in context: A103602 A205796 A081585 * A273316 A101990 A147170
KEYWORD
nonn
AUTHOR
K. D. Bajpai, Sep 19 2013
STATUS
approved