login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A005912 Truncated cube numbers.
(Formerly M5312)
2
1, 56, 311, 920, 2037, 3816, 6411, 9976, 14665, 20632, 28031, 37016, 47741, 60360, 75027, 91896, 111121, 132856, 157255, 184472, 214661, 247976, 284571, 324600, 368217, 415576, 466831, 522136, 581645, 645512, 713891, 786936, 864801, 947640, 1035607, 1128856 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

REFERENCES

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

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

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.

B. K. Teo and N. J. A. Sloane, Magic numbers in polygonal and polyhedral clusters, Inorgan. Chem. 24 (1985), 4545-4558.

Index entries for linear recurrences with constant coefficients, signature (4, -6, 4, -1).

FORMULA

a(n) = (3*n+1)^3-8*(n)*(n+1)*(n+2)/6=77/3*n^3+23*n^2+19/3*n+1.

a(0)=1, a(1)=56, a(2)=311, a(3)=920, a(n)=4*a(n-1)-6*a(n-2)+ 4*a(n-3)- a(n-4). - Harvey P. Dale, Aug 14 2011

MAPLE

A005912:=(1+52*z+93*z**2+8*z**3)/(z-1)**4; # [Conjectured by Simon Plouffe in his 1992 dissertation.]

MATHEMATICA

Table[(3n+1)^3-8(n)(n+1)(n+2)/6, {n, 0, 30}] (* or *) LinearRecurrence[ {4, -6, 4, -1}, {1, 56, 311, 920}, 30] (* Harvey P. Dale, Aug 14 2011 *)

PROG

(Haskell)

a005912 n = (n * (n * (77 * n + 69) + 19) + 3) `div` 3 :: Integer

-- Reinhard Zumkeller, Aug 09 2014

(MAGMA) [(3*n+1)^3-8*(n)*(n+1)*(n+2)/6: n in [0..40]] // Vincenzo Librandi, Aug 09 2014

(PARI) a(n)=(3*n+1)^3-8*(n)*(n+1)*(n+2)/6 \\ Charles R Greathouse IV, Feb 10 2017

CROSSREFS

Sequence in context: A110554 A253922 A220015 * A264581 A220202 A104677

Adjacent sequences:  A005909 A005910 A005911 * A005913 A005914 A005915

KEYWORD

nonn,easy,nice

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Dec 22 1999

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 25 08:15 EDT 2019. Contains 321469 sequences. (Running on oeis4.)