cp's OEIS Frontend

A333637 The number of cells which contain multiple squares of a Genealodron formed from 2^n - 1 equal-sized squares (when viewed from above).

%I A333637 #19 Jul 08 2020 20:48:03
%S A333637 0,0,0,2,7,15,27,41,57,75,95,117,141,167,195,225,257,291,327,365,405,
%T A333637 447,491,537,585,635,687,741,797,855,915,977,1041,1107,1175,1245,1317,
%U A333637 1391,1467,1545,1625,1707,1791,1877,1965,2055,2147,2241,2337,2435,2535,2637,2741,2847,2955,3065,3177,3291,3407,3525
%N A333637 The number of cells which contain multiple squares of a Genealodron formed from 2^n - 1 equal-sized squares (when viewed from above).
%C A333637 See A179178 for the definition of a Genealodron. In this variation, a Genealodron is a rooted binary tree constructed from squares. One edge of each square is attached to its parent and the two adjacent edges to its child trees.
%C A333637 The first Genealodron consists of one square.
%C A333637 The second Genealodron is formed by joining another equal-sized square to the left edge and to the right edge of the first so that the second Genealodron is made up of three squares.
%C A333637 The third Genealodron is formed by joining squares to the upper and lower edges of both the second and third square of the second Genealodron so that the third Genealodron is made up of seven squares.
%C A333637 This continues, with the edges to which the new squares are attached alternating between left/right and upper/lower.
%C A333637 From the fourth generation onwards, some squares will overlap. a(n) is the number of cells which contain overlapping squares.
%H A333637 Andrew Smith, <a href="/A297103/a297103_3.pdf">Illustration of initial terms</a>
%F A333637 Conjecture: for n>=6, a(n) = n^2 - n - 15. - _Vaclav Kotesovec_, Apr 07 2020
%F A333637 Conjectures from _Colin Barker_, Apr 07 2020: (Start)
%F A333637 G.f.: x^4*(1 + x^2)*(2 + x - 2*x^2) / (1 - x)^3.
%F A333637 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>8.
%F A333637 (End)
%Y A333637 Cf. A179178, A179316, A297103.
%K A333637 nonn,easy
%O A333637 1,4
%A A333637 _Andrew Smith_, Mar 30 2020