



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
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OFFSET

0,2


COMMENTS

Permutations avoiding 123 that contain the pattern 321 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 3subset of an (2n+1)set X then, for n>=1, a(n1) is the number of (2n1)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 21, arXiv:math.CO/0202219.
Index entries for linear recurrences with constant coefficients, signature (3,3,1).


FORMULA

a(n) = a(n1) + 4*n + 3 (with a(0)=0). [Vincenzo Librandi, Nov 17 2010]
G.f.: x*(73*x)/(1x)^3; also, a(n) = 3*a(n1)  3*a(n2) + a(n3), 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



