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A092439 Sequence arising from enumeration of domino tilings of Aztec Pillow-like regions.

%I A092439 #31 Sep 01 2025 16:54:48
%S A092439 0,0,6,30,140,560,2058,7098,23472,75372,237182,735878,2260596,6896136,
%T A092439 20933778,63325170,191089112,575626052,1731858246,5206059774,
%U A092439 15640198620,46966732320,140996664986,423191320490,1269993390720
%N A092439 Sequence arising from enumeration of domino tilings of Aztec Pillow-like regions.
%D A092439 James 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).
%H A092439 James Propp, <a href="http://faculty.uml.edu/jpropp/articles.html">Publications and Preprints</a>
%H A092439 James Propp, Enumeration of matchings: problems and progress, in L. J. Billera et al. (eds.), <a href="https://library.slmath.org/books/Book38/contents.html">New Perspectives in Algebraic Combinatorics</a>
%H A092439 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (9,-30,42,-9,-39,40,-12).
%F A092439 a(n) = (3^(n+2)+(-1)^(n+2))/2-2^(n+2)-(n+2)*(2^(n+1)-1)+(n+1)^2.
%F A092439 a(n) = A092437(n, n+2), for n >= 2.
%F A092439 a(n) = A046717(n+2)-2^(n+2)-(n+2)*(2^(n+1)-1)+(n+1)^2.
%F A092439 a(n) = 9*a(n-1)-30*a(n-2)+42*a(n-3)-9*a(n-4)-39*a(n-5)+40*a(n-6)-12*a(n-7). - _Harvey P. Dale_, Nov 27 2011
%F A092439 G.f.: 2*x^2*(6*x^4-26*x^3+25*x^2-12*x+3)/((x-1)^3*(x+1)*(2*x-1)^2*(3*x-1)). - _Colin Barker_, Nov 22 2012
%F A092439 E.g.f.: exp(x)*(4*x + x^2 - 4*(2 + x)*cosh(x) - 4*(2 + x)*sinh(x) + 2*(2*cosh(x) + sinh(x))^2). - _Stefano Spezia_, Sep 01 2025
%e A092439 a(3) = (3^5+(-1)^5)/2 - 2^5 - 5*(2^4-1) + 4^2 = 30.
%t A092439 Table[(3^(n+2)+(-1)^(n+2))/2-2^(n+2)-(n+2)(2^(n+1)-1)+(n+1)^2,{n,0,30}] (* or *) LinearRecurrence[{9,-30,42,-9,-39,40,-12},{0,0,6,30,140,560,2058},30] (* _Harvey P. Dale_, Nov 27 2011 *)
%Y A092439 Cf. A046717, A092437-A092443.
%K A092439 easy,nonn,changed
%O A092439 0,3
%A A092439 Christopher Hanusa (chanusa(AT)math.washington.edu), Mar 24 2004