|
| |
|
|
A006564
|
|
Icosahedral numbers: n(5n^2 -5n + 2)/2.
(Formerly M4837)
|
|
8
|
|
|
|
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 S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
_Simon Plouffe_, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 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] (* From 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]
|
|
|
CROSSREFS
|
Cf. A000292, A000578, A005900, A006566
Sequence in context: A135453 A165280 A173548 * A059162 A190622 A117027
Adjacent sequences: A006561 A006562 A006563 * A006565 A006566 A006567
|
|
|
KEYWORD
|
nonn,nice,easy
|
|
|
AUTHOR
|
N. J. A. Sloane.
|
|
|
STATUS
|
approved
|
| |
|
|
