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A006564 Icosahedral numbers: n(5n^2 -5n + 2)/2.
(Formerly M4837)
9
1, 12, 48, 124, 255, 456, 742, 1128, 1629, 2260, 3036, 3972, 5083, 6384, 7890, 9616, 11577, 13788, 16264, 19020, 22071, 25432, 29118, 33144, 37525, 42276, 47412, 52948, 58899, 65280, 72106, 79392, 87153, 95404, 104160, 113436, 123247, 133608 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Schlaefli symbol for this polyhedron: {3,5}

One of the 5 Platonic polyhedral (tetrahedral, cube, octahedral, dodecahedral and icosahedral) numbers (cf. A053012). [From Daniel Forgues, May 14 2010]

REFERENCES

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

T. D. Noe, Table of n, a(n) for n=1..1000

Hyun Kwang Kim, On Regular Polytope Numbers

Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992.

Simon Plouffe, 1031 Generating Functions and Conjectures, Université du Québec à Montréal, 1992.

FORMULA

a(n) = C(n+2,3) + 8 C(n+1,3) + 6 C(n,3)

a(0)=1, a(1)=12, a(2)=48, a(3)=124, a(n)=4*a(n-1)-6*a(n-2)+4*a(n-3)- a(n-4) [From Harvey P. Dale, May 26 2011]

G.f.: x*(6*x^2+8*x+1)/(x-1)^4 [From Harvey P. Dale, May 26 2011]

MAPLE

A006564:=(1+8*z+6*z**2)/(z-1)**4; [Conjectured by Simon Plouffe in his 1992 dissertation.]

MATHEMATICA

Table[n (5n^2-5n+2)/2, {n, 40}] (* or *) LinearRecurrence[{4, -6, 4, -1}, {1, 12, 48, 124}, 40] (* Harvey P. Dale, May 26 2011 *)

PROG

(MAGMA) [(5*n^3-5*n^2+2*n)/2: n in [1..100]] [From Vincenzo Librandi, Nov 21 2010]

(Haskell)

a006564 n = n * (5 * n * (n - 1) + 2) `div` 2

-- Reinhard Zumkeller, Jun 16 2013

CROSSREFS

Cf. A000292, A000578, A005900, A006566.

Cf. A000566.

Sequence in context: A135453 A165280 A173548 * A239352 A059162 A190622

Adjacent sequences:  A006561 A006562 A006563 * A006565 A006566 A006567

KEYWORD

nonn,nice,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified November 23 19:50 EST 2014. Contains 249865 sequences.