

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

Table of n, a(n) for n=0..30.
Kival Ngaokrajang, Illustration of initial terms
Index entries for linear recurrences with constant coefficients, signature (4,5,2).


FORMULA

a(0) = 1, for n >= 1, a(n) = 6*A000225(n) + a(n1).
From Colin Barker, Sep 21 2014: (Start)
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

Cf. A000225, A061777, A003215, A247618, A247619.
Sequence in context: A299262 A001296 A000970 * A240156 A155245 A155291
Adjacent sequences: A247617 A247618 A247619 * A247621 A247622 A247623


KEYWORD

nonn,easy


AUTHOR

Kival Ngaokrajang, Sep 21 2014


EXTENSIONS

More terms from Colin Barker, Sep 21 2014


STATUS

approved



