A010482 -id:A010482 - cp's OEIS frontend

A386460 Decimal expansion of the surface area of an augmented truncated cube with unit edges.

3, 4, 3, 3, 8, 2, 8, 8, 0, 4, 6, 4, 3, 7, 5, 8, 2, 3, 6, 8, 5, 9, 9, 2, 2, 6, 2, 6, 6, 6, 1, 4, 5, 9, 7, 8, 8, 6, 5, 2, 5, 1, 3, 4, 5, 1, 5, 2, 0, 0, 6, 2, 2, 6, 1, 5, 9, 3, 4, 2, 1, 8, 3, 1, 8, 2, 6, 3, 1, 2, 3, 8, 3, 5, 3, 4, 7, 4, 7, 0, 4, 9, 9, 7, 4, 7, 3, 1, 3, 9

Offset: 2

Paolo Xausa, Jul 23 2025

The augmented truncated cube is Johnson solid J_66.

			34.33828804643758236859922626661459788652513451520...

Paolo Xausa, Table of n, a(n) for n = 2..10000
Wikipedia, Augmented truncated cube.

Cf. A386459 (volume).

Cf. A002193, A010482, A386412, A386461.

First[RealDigits[15 + Sqrt[200] + Sqrt[27], 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J66", "SurfaceArea"], 10, 100]]

Equals 15 + 10*sqrt(2) + 3*sqrt(3) = 15 + 10*A002193 + A010482.

Equals the largest root of x^4 - 60*x^3 + 896*x^2 + 120*x - 21596.

A041042 Numerators of continued fraction convergents to sqrt(27).

Original entry on oeis.org

5, 26, 265, 1351, 13775, 70226, 716035, 3650401, 37220045, 189750626, 1934726305, 9863382151, 100568547815, 512706121226, 5227629760075, 26650854921601, 271736178976085, 1385331749802026, 14125053676996345

Offset: 0

N. J. A. Sloane

Subset of |A002316| (conjectured).

Vincenzo Librandi, Table of n, a(n) for n = 0..200
Index entries for linear recurrences with constant coefficients, signature (0,52,0,-1).

Cf. A010482, A041043, A002316.

Table[Numerator[FromContinuedFraction[ContinuedFraction[Sqrt[27],n]]],{n,1,50}] (* Vladimir Joseph Stephan Orlovsky, Mar 18 2011*)
Numerator/@Convergents[Sqrt[27],20] (* Harvey P. Dale, Jul 21 2011 *)
CoefficientList[Series[(- x^3 + 5 x^2 + 26 x + 5)/(x^4 - 52 x^2 + 1), {x, 0, 30}], x]  (* Vincenzo Librandi, Oct 28 2013 *)
a0[n_] := (-5-3*Sqrt[3]+(-5+3*Sqrt[3])*(26+15*Sqrt[3])^(2*n))/(2*(26+15*Sqrt[3])^n) // Simplify
a1[n_] := (1+(26+15*Sqrt[3])^(2*n))/(2*(26+15*Sqrt[3])^n) //  Simplify
Flatten[MapIndexed[{a0[#], a1[#]}&,Range[10]]] (* Gerry Martens, Jul 10 2015 *)
LinearRecurrence[{0,52,0,-1},{5,26,265,1351},30] (* Harvey P. Dale, Dec 12 2015 *)

G.f.: (-x^3+5x^2+26x+5)/(x^4-52x^2+1).
From Gerry Martens, Jul 11 2015: (Start)
Interspersion of 2 sequences [a0(n),a1(n)]:
a0(n) = ((-5-3*sqrt(3))/(26+15*sqrt(3))^n+(-5+3*sqrt(3))*(26+15*sqrt(3))^n)/2.
a1(n) = (1/(26+15*sqrt(3))^n+(26+15*sqrt(3))^n)/2. (End)

A374948 Decimal expansion of the Euclidean length of the minimum Steiner tree joining all the vertices of a unit cube.

Original entry on oeis.org

6, 1, 9, 6, 1, 5, 2, 4, 2, 2, 7, 0, 6, 6, 3, 1, 8, 8, 0, 5, 8, 2, 3, 3, 9, 0, 2, 4, 5, 1, 7, 6, 1, 7, 1, 0, 0, 8, 2, 8, 4, 1, 5, 7, 6, 1, 4, 3, 1, 1, 4, 1, 8, 8, 4, 1, 6, 7, 4, 2, 0, 9, 3, 8, 3, 5, 5, 7, 9, 9, 0, 5, 0, 7, 2, 6, 4, 0, 0, 1, 1, 1, 2, 4, 3, 4, 3

Offset: 1

Marco Ripà, Jul 24 2024

The 1994 Bridge's paper entitled "Minimal Steiner Trees for Three Dimensional Networks" (see Links) suggested an optimal strategy to solve the minimum Steiner tree problem for the unit cube {0,1}^3, and the total length of the provided Steiner Tree is 1 + 3*sqrt(3).

Also the surface area of a gyroelongated square pyramid (Johnson solid J_10) with unit edges. - Paolo Xausa, Aug 04 2025

			6.1961524227066318805823390245176171008284157614311418841674209383...

R. Bridges, Minimal Steiner Trees for Three Dimensional Networks, Math. Gaz., 78 (1994), 157-162.
Math Overflow, Joining the 2^k points of {0,1}^k with the shortest tree.
Mathematics Stack Exchange, Steiner tree problem in 3D.
J. M. Smith, R. Weiss, and M. Patel, An O(N2) Heuristic for Steiner Minimal Trees in E3, Networks 26 (1995), 273-289.
B. Toppur and J. M. A. Smith, A Sausage Heuristic for Steiner Minimal Trees in Three-Dimensional Euclidean Space, J. Math. Modelling and Algorithms, 4 (2005), 199-217.
Wikipedia, Gyroelongated square pyramid.

Cf. A002194, A010482, A374148, A374260.

Essentially the same as A178809, A176532 and A010482.

RealDigits[3Sqrt[3]+1,10,87][[1]] (* Stefano Spezia, Jul 25 2024 *)

Equals 3*sqrt(3) + 1.

Equals A010482(n) for any n >= 2 and a(1) = A010482(1) + 1.

A386739 Decimal expansion of the volume of a sphenocorona with unit edges.

Original entry on oeis.org

1, 5, 1, 5, 3, 5, 1, 6, 3, 9, 9, 7, 6, 4, 0, 6, 5, 5, 9, 7, 2, 8, 4, 7, 9, 3, 1, 2, 4, 7, 1, 8, 1, 2, 9, 0, 4, 8, 2, 2, 8, 6, 9, 5, 0, 6, 8, 0, 8, 7, 9, 4, 2, 6, 6, 7, 5, 9, 9, 0, 4, 6, 3, 0, 5, 1, 0, 3, 0, 9, 2, 7, 0, 6, 4, 4, 3, 2, 9, 3, 0, 7, 9, 9, 0, 9, 2, 3, 6, 5

Offset: 1

Paolo Xausa, Aug 01 2025

The sphenocorona is Johnson solid J_86.

			1.5153516399764065597284793124718129048228695068...

Paolo Xausa, Table of n, a(n) for n = 1..10000
Wikipedia, Sphenocorona.

Cf. A010482 (surface area - 2), A178809 (surface area + 4).

Cf. A010507, A020775, A115754, A386740, A386741.

First[RealDigits[Sqrt[1 + 3*Sqrt[3/2] + Sqrt[13 + Sqrt[54]]]/2, 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J86", "Volume"], 10, 100]]

Equals sqrt(1 + 3*sqrt(3/2) + sqrt(13 + 3*sqrt(6)))/2 = sqrt(1 + 3*A115754  + sqrt(13 + A010507))/2.
Equals A386740 - A020775.
Equals the largest real root of 1024*x^8 - 1024*x^6 - 3008*x^4 - 96*x^2 + 9.

A176532 Decimal expansion of 5+3*sqrt(3).

Original entry on oeis.org

1, 0, 1, 9, 6, 1, 5, 2, 4, 2, 2, 7, 0, 6, 6, 3, 1, 8, 8, 0, 5, 8, 2, 3, 3, 9, 0, 2, 4, 5, 1, 7, 6, 1, 7, 1, 0, 0, 8, 2, 8, 4, 1, 5, 7, 6, 1, 4, 3, 1, 1, 4, 1, 8, 8, 4, 1, 6, 7, 4, 2, 0, 9, 3, 8, 3, 5, 5, 7, 9, 9, 0, 5, 0, 7, 2, 6, 4, 0, 0, 1, 1, 1, 2, 4, 3, 4, 3, 8, 5, 6, 0, 2, 7, 1, 7, 4, 5, 7, 2, 7, 0, 2, 6, 8

Offset: 2

Klaus Brockhaus, Apr 24 2010

Continued fraction expansion of 5+3*sqrt(3) is A010721 preceded by 10.

a(n) = A010482(n-2) for n > 3.

			5+3*sqrt(3) = 10.19615242270663188058...

Cf. A002194 (decimal expansion of sqrt(3)), A010482 (decimal expansion of sqrt(27)), A010721 (repeat 5, 10).

RealDigits[5+3Sqrt[3],10,120][[1]] (* Harvey P. Dale, May 30 2012 *)

A386695 Decimal expansion of the volume of a snub disphenoid with unit edges.

Original entry on oeis.org

8, 5, 9, 4, 9, 3, 6, 4, 6, 1, 9, 1, 3, 0, 0, 5, 3, 1, 5, 5, 5, 4, 0, 9, 6, 3, 6, 9, 7, 9, 7, 3, 6, 3, 9, 2, 7, 0, 7, 4, 9, 7, 2, 2, 0, 5, 8, 7, 6, 9, 3, 3, 6, 1, 9, 0, 4, 0, 1, 9, 5, 2, 6, 5, 8, 5, 8, 1, 4, 3, 0, 7, 3, 7, 7, 1, 2, 6, 7, 8, 3, 5, 4, 2, 7, 0, 9, 4, 6, 7

Offset: 0

Paolo Xausa, Jul 31 2025

The snub disphenoid is Johnson solid J_84.

			0.85949364619130053155540963697973639270749722...

Paolo Xausa, Table of n, a(n) for n = 0..10000
Wikipedia, Snub disphenoid.

Cf. A010482 (surface area).

Cf. A386696.

First[RealDigits[Root[5832*#^6 - 1377*#^4 - 2160*#^2 - 4 &, 2], 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J84", "Volume"], 10, 100]]

Equals the largest real root of 5832*x^6 - 1377*x^4 - 2160*x^2 - 4.

A171542 Decimal expansion of sqrt(27/70).

Original entry on oeis.org

6, 2, 1, 0, 5, 9, 0, 0, 3, 4, 0, 8, 1, 1, 8, 7, 9, 6, 0, 1, 6, 5, 1, 4, 1, 7, 8, 1, 6, 4, 4, 1, 8, 7, 8, 8, 1, 3, 4, 5, 7, 7, 1, 2, 3, 2, 0, 3, 9, 5, 5, 9, 8, 9, 5, 1, 5, 5, 3, 9, 6, 3, 4, 5, 9, 0, 7, 7, 7, 6, 1, 5, 9, 7, 0, 8, 7, 2, 0, 1, 8, 0, 7, 3, 3, 9, 5, 5, 6, 5, 3, 7, 1, 5, 8, 3, 6, 0, 7, 0, 4, 6, 5, 5, 9

Offset: 0

R. J. Mathar, Dec 11 2009

The absolute value of the Clebsch-Gordan coupling coefficient = <2 3/2 ; -1 3/2 | 5/2 1/2>.

			sqrt(27/70) = 3*sqrt(210)/70 = 0.621059003408118796016514178164...

Daniel Starodubtsev, Table of n, a(n) for n = 0..10000
Wikipedia, Table of Clebsch-Gordan coefficients

Cf. A010482, A010522, A010541, A171537.

RealDigits[Sqrt[27/70],10,120][[1]] (* Harvey P. Dale, Apr 26 2011 *)

Equals A010482/A010522 = A010541*A171537/10.

A370562 Decimal expansion of (2Pi - 3sqrt(3))/2.

Original entry on oeis.org

5, 4, 3, 5, 1, 6, 4, 4, 2, 2, 3, 6, 4, 7, 7, 2, 9, 8, 1, 7, 1, 4, 7, 3, 8, 7, 1, 0, 2, 0, 6, 9, 4, 3, 3, 3, 7, 8, 2, 9, 6, 1, 5, 1, 8, 6, 5, 9, 5, 3, 4, 8, 7, 8, 8, 9, 1, 2, 3, 4, 1, 2, 3, 1, 2, 9, 9, 1, 6, 8, 8, 0, 9, 2, 3, 0, 0, 8, 9, 4, 3, 0

Offset: 0

Wolfdieter Lang, Mar 15 2024

This constant is the difference of the area of a disk with radius 1 (length unit) and the inscribed regular hexagon.

			0.5435164422364772981714738710206943337829615186595348788912...

Cf. A000796, A019692, A010482, A104956, A248897.

RealDigits[Pi - 3*Sqrt[3]/2, 10, 120][[1]] (* Amiram Eldar, Mar 15 2024 *)

Equals (A019692 - A010482)/2.

Equals Pi - 3*sqrt(3)/2 = A000796 - A104956.

A375741 Decimal expansion of 6Pi/(3sqrt(3) + 8*Pi).

Original entry on oeis.org

6, 2, 1, 5, 0, 4, 8, 9, 6, 8, 8, 7, 4, 3, 1, 5, 9, 1, 4, 0, 5, 9, 6, 7, 8, 1, 8, 8, 0, 8, 0, 2, 8, 2, 7, 3, 1, 2, 7, 0, 7, 8, 8, 5, 1, 1, 5, 8, 5, 3, 4, 2, 9, 4, 0, 7, 0, 2, 8, 0, 6, 9, 9, 4, 5, 3, 1, 1, 4, 7, 4, 8, 1, 2, 5, 0, 6, 4, 4, 9, 6, 2, 2, 2, 6, 7, 4, 4, 5, 9, 9, 2, 9, 8, 0, 7, 6, 0, 6, 8

Offset: 0

Stefano Spezia, Aug 26 2024

This constant expresses the expected proportion of individuals that belong to reciprocal nearest-neighbor relationship pairs in a population of random patterns over a plane.

			0.62150489688743159140596781880802827312707885...

E. C. Pielou, An Introduction to Mathematical Ecology, John Wiley & Sons, Inc. 1969. See pp. 121-122.

Index entries for transcendental numbers.

Cf. A000796, A010482, A010527, A019692, A019699, A228719, A228824.

RealDigits[6Pi/(3Sqrt[3]+8Pi),10,100][[1]]

Equals Integral_{x=0..oo} 2*Pi*x*exp(-x^2*(sqrt(3)/2+4*Pi/3)) dx. [Pielou, 1969]

A379392 Decimal expansion of 3sqrt(3)/(4Pi^2).

Original entry on oeis.org

1, 3, 1, 6, 2, 0, 0, 7, 8, 4, 6, 3, 6, 5, 9, 2, 4, 2, 8, 4, 2, 5, 5, 2, 5, 9, 4, 0, 2, 7, 2, 3, 3, 5, 8, 6, 1, 6, 6, 2, 3, 0, 0, 4, 1, 6, 2, 1, 9, 2, 6, 6, 3, 6, 4, 7, 9, 8, 2, 9, 8, 7, 9, 7, 7, 4, 2, 0, 3, 7, 0, 8, 8, 4, 1, 0, 8, 0, 3, 4, 1, 2, 8, 1, 7, 4, 1, 4, 4, 0, 0, 4, 1, 8, 6, 4, 9, 7, 1, 7

Offset: 0

Stefano Spezia, Dec 22 2024

			0.13162007846365924284255259402723358616623004162...

Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 8.4.2, p. 494.

Cf. A002194, A002388, A010482, A212002, A240935.

RealDigits[3Sqrt[3]/(4Pi^2),10,100][[1]]

Equals A240935/Pi. - Hugo Pfoertner, Dec 22 2024

cp's OEIS Frontend

A386460 Decimal expansion of the surface area of an augmented truncated cube with unit edges.

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A041042 Numerators of continued fraction convergents to sqrt(27).

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A374948 Decimal expansion of the Euclidean length of the minimum Steiner tree joining all the vertices of a unit cube.

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A386739 Decimal expansion of the volume of a sphenocorona with unit edges.

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A176532 Decimal expansion of 5+3*sqrt(3).

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A386695 Decimal expansion of the volume of a snub disphenoid with unit edges.

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A171542 Decimal expansion of sqrt(27/70).

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A370562 Decimal expansion of (2*Pi - 3*sqrt(3))/2.

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A370562 Decimal expansion of (2Pi - 3sqrt(3))/2.

A375741 Decimal expansion of 6Pi/(3sqrt(3) + 8*Pi).

A379392 Decimal expansion of 3sqrt(3)/(4Pi^2).