A224837 Surface area of Johnson square pyramid (rounded down) with all the edge-lengths equal to n.

2, 10, 24, 43, 68, 98, 133, 174, 221, 273, 330, 393, 461, 535, 614, 699, 789, 885, 986, 1092, 1204, 1322, 1445, 1573, 1707, 1846, 1991, 2141, 2297, 2458, 2625, 2797, 2975, 3158, 3346, 3540, 3740, 3945, 4155, 4371, 4592, 4819, 5051, 5289, 5532, 5781, 6035, 6294

Offset

1,1

Comments

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

Links

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

Wikipedia, Square pyramid

Formula

a(n) = floor((1+sqrt(3))*n^2).

Example

a(3)=24: Surface area = (1+sqrt(3))*k^2 = (1+sqrt(3))*3^2 = 24.58845727 and floor(24.58845727) = 24.

Maple

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

Mathematica

Table[Floor[(1+Sqrt[3])*k^2], {k, 500}]

Prog

(PARI) vector(500, k, floor((1+sqrt(3))*k^2))
(PARI) a(n)=n^2+sqrtint(3*n^4) \\ Charles R Greathouse IV, Sep 18 2013

Crossrefs

Cf. A090388, A228189.

Sequence in context: A120845 A330280 A293412 * A049450 A092906 A244383

Adjacent sequences: A224834 A224835 A224836 * A224838 A224839 A224840

Keyword

nonn

Author

K. D. Bajpai, Sep 18 2013

Status

approved