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A224837 Surface area of Johnson square pyramid (rounded down) with all the edge-lengths equal to n. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified February 4 05:49 EST 2023. Contains 360046 sequences. (Running on oeis4.)