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A247620 Start with a single hexagon; at n-th generation add a hexagon at each expandable vertex; a(n) is the sum of all label values at n-th 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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
Inspired by A061777, let us assign the label "1" to an origin hexagon; at n-th 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 non-overlapping 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(n-1))/6 is A000225
LINKS
FORMULA
a(0) = 1, for n >= 1, a(n) = 6*A000225(n) + a(n-1).
From Colin Barker, Sep 21 2014: (Start)
a(n) = (-11+3*2^(2+n)-6*n).
a(n) = 4*a(n-1)-5*a(n-2)+2*a(n-3).
G.f.: -(x+1)*(2*x+1) / ((x-1)^2*(2*x-1)).
(End)
PROG
(PARI) a(n) = if (n<1, 1, 6*(2^n-1)+a(n-1))
for (n=0, 50, print1(a(n), ", "))
(PARI) Vec(-(x+1)*(2*x+1)/((x-1)^2*(2*x-1)) + O(x^100)) \\ Colin Barker, Sep 21 2014
CROSSREFS
Sequence in context: A299262 A001296 A000970 * A240156 A155245 A155291
KEYWORD
nonn,easy
AUTHOR
Kival Ngaokrajang, Sep 21 2014
EXTENSIONS
More terms from Colin Barker, Sep 21 2014
STATUS
approved

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Last modified April 25 10:51 EDT 2024. Contains 371967 sequences. (Running on oeis4.)