

A033585


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


24



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
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OFFSET

0,2


COMMENTS

If Y is a fixed 3subset of a (4n+1)set X then a(n) is the number of (4n1)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.
Amelia Carolina Sparavigna, The groupoids of Mersenne, Fermat, Cullen, Woodall and other Numbers and their representations by means of integer sequences, Politecnico di Torino, Italy (2019), [math.NT].
Amelia Carolina Sparavigna, The groupoid of the Triangular Numbers and the generation of related integer sequences, Politecnico di Torino, Italy (2019).
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(n1)  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)/(x1)^3 .  R. J. Mathar, Feb 06 2017
E.g.f.: (8*x^2 + 10*x)*exp(x).  G. C. Greubel, Jul 18 2017
From Amiram Eldar, Jul 22 2020: (Start)
Sum_{n>=1} 1/a(n) = 2  Pi/4  3*log(2)/2.
Sum_{n>=1} (1)^(n+1)/a(n) = sqrt(2)*Pi/4 + sqrt(2)*arcsinh(1)/2 + log(2)/2  2. (End)


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: A271912 A288947 A328146 * A118629 A050509 A211057
Adjacent sequences: A033582 A033583 A033584 * A033586 A033587 A033588


KEYWORD

nonn,easy


AUTHOR

N. J. A. Sloane


STATUS

approved



