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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A081266 Staggered diagonal of triangular spiral in A051682. 16
0, 6, 21, 45, 78, 120, 171, 231, 300, 378, 465, 561, 666, 780, 903, 1035, 1176, 1326, 1485, 1653, 1830, 2016, 2211, 2415, 2628, 2850, 3081, 3321, 3570, 3828, 4095, 4371, 4656, 4950, 5253, 5565, 5886, 6216, 6555, 6903, 7260, 7626, 8001, 8385, 8778, 9180 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Staggered diagonal of triangular spiral in A051682, between (0,4,17) spoke and (0,7,23) spoke.

Binomial transform of (0, 6, 9, 0, 0, 0, ...).

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

a(n) = A000217(3*n); a(2*n) = A144314(n). - Reinhard Zumkeller, Sep 17 2008

LINKS

Table of n, a(n) for n=0..45.

Milan Janjic, Two Enumerative Functions

M. Janjic and B. Petkovic, A Counting Function, arXiv 1301.4550, 2013

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

FORMULA

a(n) = 6*C(n,1) + 9*C(n,2).

a(n) = 3*n*(3*n+1)/2.

G.f.: (6*x+3*x^2)/(1-x)^3.

a(n) = 3*A005449(n). - R. J. Mathar, Mar 27 2009

a(n) = 9*n+a(n-1)-3 for n>0, a(0)=0. - Vincenzo Librandi, Aug 08 2010

a(n) = A218470(9n+5). - Philippe Deléham, Mar 27 2013

a(n) = sum( (-1)^(n+k)*k^2, k=0..3n ). - Bruno Berselli, Aug 29 2013

EXAMPLE

a(1)=9*1+0-3=6, a(2)=9*2+6-3=21, a(3)=9*3+21-3=45.

For n=3, a(3) = -0^2+1^2-2^2+3^2-4^2+5^2-6^2+7^2-8^2+9^2 = 45.

MAPLE

seq(binomial(3*n+1, 2), n=0..45); # Zerinvary Lajos, Jan 21 2007

a:=n->sum(j, j=0..n): seq(a(3*n), n=0..45); # Zerinvary Lajos, Apr 30 2007

MATHEMATICA

s=0; lst={s}; Do[s+=n++ +6; AppendTo[lst, s], {n, 0, 7!, 9}]; lst (* Vladimir Joseph Stephan Orlovsky, Nov 16 2008 *)

LinearRecurrence[{3, -3, 1}, {0, 6, 21}, 50] (* Harvey P. Dale, Aug 29 2015 *)

PROG

(PARI) a(n)=3*n*(3*n+1)/2 \\ Charles R Greathouse IV, Jun 17 2017

CROSSREFS

Cf. A000290, A014105, A022266, A033585, A062725, A144312.

Sequence in context: A180857 A119868 A175729 * A087863 A212656 A051941

Adjacent sequences:  A081263 A081264 A081265 * A081267 A081268 A081269

KEYWORD

nonn,easy

AUTHOR

Paul Barry, Mar 15 2003

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 October 23 03:37 EDT 2018. Contains 316519 sequences. (Running on oeis4.)