The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A092443 Sequence arising from enumeration of domino tilings of Aztec Pillow-like regions. 7
 3, 12, 50, 210, 882, 3696, 15444, 64350, 267410, 1108536, 4585308, 18929092, 78004500, 320932800, 1318498920, 5409723510, 22169259090, 90751353000, 371125269900, 1516311817020, 6189965556060, 25249187564640 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The sequence 1,3,12,50,... is ((n+2)/2)C(2n,n) with g.f. F(1/2,3;2;4x). - Paul Barry, Sep 18 2008 REFERENCES J. Propp, Enumeration of matchings: problems and progress, pp. 255-291 in L. J. Billera et al., eds, New Perspectives in Algebraic Combinatorics, Cambridge, 1999 (see Problem 13). LINKS Michael De Vlieger, Table of n, a(n) for n = 1..1659 Sanjay Moudgalya, Abhinav Prem, Rahul Nandkishore, Nicolas Regnault, B. Andrei Bernevig, Thermalization and its absence within Krylov subspaces of a constrained Hamiltonian, arXiv:1910.14048 [cond-mat.str-el], 2019. J. Propp, Publications and Preprints J. Propp, Enumeration of matchings: problems and progress, in L. J. Billera et al. (eds.), New Perspectives in Algebraic Combinatorics FORMULA a(n) = (2*n-1)!/((n-1)!)^2+(2*n)!/(n!)^2; A056347(n) = A002457(n-1) + A000984(n). a(n) = (n+2)*A001700(n-1). - Vladeta Jovovic, Jul 12 2004 n*a(n) + (-7*n+4)*a(n-1) + 6*(2*n-3)*a(n-2) = 0. - R. J. Mathar, Nov 30 2012 EXAMPLE a(3) = 5!/2!2! + 6!/3!3! = 50. MATHEMATICA Array[Binomial[2 # + 1, # + 1] &[# - 1]*(# + 2) &, 22] (* Michael De Vlieger, Dec 17 2017 *) PROG (MuPAD) combinat::catalan(n) *binomial(n+2, 2) \$ n = 1..22 // Zerinvary Lajos, Feb 15 2007 (PARI) a(n) = (n+2)*binomial(2*n-1, n); \\ Altug Alkan, Dec 17 2017 CROSSREFS Cf. A000984, A002457. Cf. A092437, A092438, A092439, A092440, A092441, A092442. Sequence in context: A037765 A037653 A229665 * A108080 A113441 A119976 Adjacent sequences:  A092440 A092441 A092442 * A092444 A092445 A092446 KEYWORD easy,nonn AUTHOR Christopher Hanusa (chanusa(AT)math.washington.edu), Mar 24 2004 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified June 14 12:04 EDT 2021. Contains 345025 sequences. (Running on oeis4.)