cp's OEIS Frontend

A121553 Total area of all deco polyominoes of height n. A deco polyomino is a directed column-convex polyomino in which the height, measured along the diagonal, is attained only in the last column.

%I A121553 #5 Jul 22 2022 13:22:16
%S A121553 1,4,20,122,874,7164,65988,674064,7558416,92276640,1218255840,
%T A121553 17293495680,262656570240,4250077896960,72992067321600,
%U A121553 1326101675673600,25410150701107200,512158576546713600,10832221231772774400
%N A121553 Total area of all deco polyominoes of height n. A deco polyomino is a directed column-convex polyomino in which the height, measured along the diagonal, is attained only in the last column.
%C A121553 a(n)=Sum(k*A121552(n,k), k=n..1+n(n-1)/2).
%D A121553 E. Barcucci, A. Del Lungo and R. Pinzani, "Deco" polyominoes, permutations and random generation, Theoretical Computer Science, 159, 1996, 29-42.
%F A121553 a(1)=1; a(n)=n*a(n-1)+(n-1)!*[1+n(n-1)/2] for n>=2 (see Barcucci et al. reference, p. 34).
%F A121553 a(n)=n![n(n-1)/4 + 1/1 + 1/2 + ... +1/n]. - _Emeric Deutsch_, Apr 06 2008
%F A121553 Conjecture D-finite with recurrence a(n) +(-2*n-3)*a(n-1) +(n^2+4*n-3)*a(n-2) +2*(-n^2+n+3)*a(n-3) +2*(n-3)^2*a(n-4)=0. - _R. J. Mathar_, Jul 22 2022
%p A121553 a[1]:=1: for n from 2 to 22 do a[n]:=n*a[n-1]+(n-1)!*(1+n*(n-1)/2) od: seq(a[n],n=1..22);
%Y A121553 Cf. A121552.
%K A121553 nonn
%O A121553 1,2
%A A121553 _Emeric Deutsch_, Aug 08 2006