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A033537 n*(2*n+5). 21
0, 7, 18, 33, 52, 75, 102, 133, 168, 207, 250, 297, 348, 403, 462, 525, 592, 663, 738, 817, 900, 987, 1078, 1173, 1272, 1375, 1482, 1593, 1708, 1827, 1950, 2077, 2208, 2343, 2482, 2625, 2772, 2923, 3078 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Permutations avoiding 12-3 that contain the pattern 32-1 exactly once.

a(n) = A014107(n) + 8*n^2; A100035(a(n)) = 3 for n>1. - Reinhard Zumkeller, Oct 31 2004

If Y is a 3-subset of an (2n+1)-set X then, for n>=1, a(n-1) is the number of (2n-1)-subsets of X having at least two elements in common with Y. - Milan Janjic, Dec 16 2007

LINKS

Table of n, a(n) for n=0..38.

T. Mansour, Restricted permutations by patterns of type 2-1, arXiv:math.CO/0202219.

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

FORMULA

a(n) = a(n-1) + 4*n + 3 (with a(0)=0). [Vincenzo Librandi, Nov 17 2010]

G.f.: x*(7-3*x)/(1-x)^3; also, a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3), n>=3, a(0)=0, a(1)=7, a(2)=18. - L. Edson Jeffery, Oct 14 2012

MATHEMATICA

Table[n*(2*n+5), {n, 0, 50}] (* Vladimir Joseph Stephan Orlovsky, Nov 16 2008 *)

CROSSREFS

Cf. A100036, A100037, A100038, A100039.

Sequence in context: A103572 A049532 A156619 * A225286 A000566 A225248

Adjacent sequences:  A033534 A033535 A033536 * A033538 A033539 A033540

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified December 9 23:16 EST 2016. Contains 278993 sequences.