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A093328 a(n) = 2*n^2 + 3. 15
3, 5, 11, 21, 35, 53, 75, 101, 131, 165, 203, 245, 291, 341, 395, 453, 515, 581, 651, 725, 803, 885, 971, 1061, 1155, 1253, 1355, 1461, 1571, 1685, 1803, 1925, 2051, 2181, 2315, 2453, 2595, 2741, 2891, 3045, 3203, 3365, 3531, 3701, 3875, 4053, 4235 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Number of 132-avoiding two-stack sortable permutations which also avoid 4321.

Conjecture: no perfect powers. - Zak Seidov, Sep 27 2015

Numbers k such that 2*k - 6 is a square. - Bruno Berselli, Nov 08 2017

REFERENCES

Steven Edwards and W. Griffiths, Generalizations of Delannoy and cross polytope numbers, Fib. Q., 55 (2017), 356-366.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Steven Edwards and William Griffiths, On Generalized Delannoy Numbers, J. Int. Seq., Vol. 23 (2020), Article 20.3.6.

E. S. Egge and T. Mansour, 132-avoiding Two-stack Sortable Permutations, Fibonacci Numbers, and Pell Numbers, arXiv:math/0205206 [math.CO], 2002.

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

FORMULA

From Vincenzo Librandi, Jul 08 2012: (Start)

G.f.: (3 - 4*x + 5*x^2)/(1 - x)^3.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). (End)

MATHEMATICA

Table[2 n^2 + 3, {n, 0, 100}] (* Vladimir Joseph Stephan Orlovsky, Feb 15 2011*)

CoefficientList[Series[(3 - 4 x + 5 x^2)/(1 - x)^3, {x, 0, 50}], x] (* Vincenzo Librandi, Jul 08 2012 *)

LinearRecurrence[{3, -3, 1}, {3, 5, 11}, 50] (* Harvey P. Dale, Apr 03 2016 *)

PROG

(PARI) a(n)=2*n^2+3; \\ Zak Seidov, Sep 27 2015

(MAGMA) [2*n^2+3: n in [0..50]]; // Vincenzo Librandi, Jul 08 2012

CROSSREFS

a(n) = A005893(n)+1 = A058331(n)+2 = A001105(n)+3.

a(n+2) = A154685(n+1,n+2).

Sequence in context: A074710 A057460 A269112 * A045515 A298342 A293317

Adjacent sequences:  A093325 A093326 A093327 * A093329 A093330 A093331

KEYWORD

nonn,easy

AUTHOR

Ralf Stephan, Apr 25 2004

EXTENSIONS

Simpler definition and new offset from Paul F. Brewbaker, Jun 23 2009

Edited by N. J. A. Sloane, Jun 27 2009

STATUS

approved

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Last modified September 24 17:09 EDT 2020. Contains 337321 sequences. (Running on oeis4.)