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A033585 a(n) = 2*n*(4*n+1). 20
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

Table of n, a(n) for n=0..36.

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

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 *)

CROSSREFS

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

Sequence in context: A117404 A072517 A271912 * A118629 A050509 A211057

Adjacent sequences:  A033582 A033583 A033584 * A033586 A033587 A033588

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified March 24 15:46 EDT 2017. Contains 283991 sequences.