

A247620


Start with a single hexagon; at nth generation add a hexagon at each expandable vertex; a(n) is the sum of all label values at nth generation. (See comment for construction rules.)


10



1, 7, 25, 67, 157, 343, 721, 1483, 3013, 6079, 12217, 24499, 49069, 98215, 196513, 393115, 786325, 1572751, 3145609, 6291331, 12582781, 25165687, 50331505, 100663147, 201326437, 402653023, 805306201, 1610612563, 3221225293, 6442450759, 12884901697
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OFFSET

0,2


COMMENTS

Inspired by A061777, let us assign the label "1" to an origin hexagon; at nth generation add a hexagon at each expandable vertex, i.e. a vertex such that the new added generations will not overlap to the existing ones, but overlapping among new generations are allowed. The nonoverlapping squares will have the same label value as a predecessor; for the overlapping ones, the label value will be sum of label values of predecessors. The hexagons count is A003215. See llustration. For n >= 1, (a(n)  a(n1))/6 is A000225


LINKS



FORMULA

a(0) = 1, for n >= 1, a(n) = 6*A000225(n) + a(n1).
a(n) = (11+3*2^(2+n)6*n).
a(n) = 4*a(n1)5*a(n2)+2*a(n3).
G.f.: (x+1)*(2*x+1) / ((x1)^2*(2*x1)).
(End)


PROG

(PARI) a(n) = if (n<1, 1, 6*(2^n1)+a(n1))
for (n=0, 50, print1(a(n), ", "))
(PARI) Vec((x+1)*(2*x+1)/((x1)^2*(2*x1)) + O(x^100)) \\ Colin Barker, Sep 21 2014


CROSSREFS



KEYWORD

nonn,easy


AUTHOR



EXTENSIONS



STATUS

approved



