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

 

Logo

Annual appeal: Please make a donation to keep the OEIS running! Over 6000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A033585 a(n) = 2*n*(4*n+1). 21
0, 10, 36, 78, 136, 210, 300, 406, 528, 666, 820, 990, 1176, 1378, 1596, 1830, 2080, 2346, 2628, 2926, 3240, 3570, 3916, 4278, 4656, 5050, 5460, 5886, 6328, 6786, 7260, 7750, 8256, 8778, 9316, 9870, 10440 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

If Y is a fixed 3-subset of a (4n+1)-set X then a(n) is the number of (4n-1)-subsets of X intersecting Y. - Milan Janjic, Oct 28 2007

Sequence found by reading the line from 0, in the direction 0, 10, ..., in the square spiral whose vertices are the triangular numbers A000217. - Omar E. Pol, Sep 03 2011

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..5000

Milan Janjic, Two Enumerative Functions

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

FORMULA

a(n) = 2*A007742(n).

a(n) = A000217(4*n) = A014105(2*n). - Reinhard Zumkeller, Sep 17 2008

a(n) = 16*n + a(n-1) - 6 (with a(0) = 0). - Vincenzo Librandi, Aug 05 2010

a(n) = A005843(n)*A016813(n). - Omar E. Pol, Oct 31 2013

G.f.: -2*x*(5+3*x)/(x-1)^3 . - R. J. Mathar, Feb 06 2017

E.g.f.: (8*x^2 + 10*x)*exp(x). - G. C. Greubel, Jul 18 2017

MAPLE

seq(binomial(4*n+1, 2), n=0..36); # Zerinvary Lajos, Jan 21 2007

MATHEMATICA

f[n_]:=2*n*(4*n+1); f[Range[0, 60]] (* Vladimir Joseph Stephan Orlovsky, Feb 05 2011 *)

PROG

(PARI) a(n)=2*n*(4*n+1) \\ Charles R Greathouse IV, Jun 16 2017

CROSSREFS

Cf. A081266, A144312, A144314. - Reinhard Zumkeller, Sep 17 2008

Sequence in context: A072517 A271912 A288947 * A118629 A050509 A211057

Adjacent sequences:  A033582 A033583 A033584 * A033586 A033587 A033588

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified November 21 13:53 EST 2017. Contains 295001 sequences.