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A247618 Start with a single square; at n-th generation add a square at each expandable vertex; a(n) is the sum of all label values at n-th generation. (See comment for construction rules.) 12
1, 5, 17, 45, 105, 229, 481, 989, 2009, 4053, 8145, 16333, 32713, 65477, 131009, 262077, 524217, 1048501, 2097073, 4194221, 8388521, 16777125, 33554337, 67108765, 134217625, 268435349, 536870801, 1073741709, 2147483529, 4294967173, 8589934465 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
Inspired by A061777, let us assign label "1" to an origin square; at n-th generation add a square 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 squares count is A001844. See illustration. For n >= 1, (a(n) - a(n-1))/4 is A000225.
LINKS
FORMULA
a(0) = 1, for n >= 1, a(n) = 4*A000225(n) + a(n-1).
From Colin Barker, Sep 21 2014: (Start)
a(n) = 4*a(n-1)-5*a(n-2)+2*a(n-3).
a(n) = (-7+2^(3+n)-4*n).
G.f.: -(2*x^2+x+1) / ((x-1)^2*(2*x-1)).
(End)
PROG
(PARI)
a(n) = if (n<1, 1, 4*(2^n-1)+a(n-1))
for (n=0, 50, print1(a(n), ", "))
(PARI)
Vec(-(2*x^2+x+1) / ((x-1)^2*(2*x-1)) + O(x^100)) \\ Colin Barker, Sep 21 2014
CROSSREFS
Sequence in context: A174794 A133252 A299335 * A269962 A048612 A320554
KEYWORD
nonn,easy
AUTHOR
Kival Ngaokrajang, Sep 20 2014
STATUS
approved

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Last modified March 28 20:05 EDT 2024. Contains 371254 sequences. (Running on oeis4.)