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A247619
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Start with a single pentagon; at n-th generation add a pentagon at each expandable vertex; a(n) is the sum of all label values at n-th generation. (See comment for construction rules.)
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11
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1, 6, 16, 36, 66, 116, 186, 296, 446, 676, 986, 1456, 2086, 3036, 4306, 6216, 8766, 12596, 17706, 25376, 35606, 50956, 71426, 102136, 143086, 204516, 286426, 409296, 573126, 818876, 1146546, 1638056, 2293406, 3276436, 4587146, 6553216, 9174646, 13106796
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OFFSET
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0,2
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COMMENTS
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Inspired by A061777, let us assign the label "1" to an origin pentagon; at n-th generation add a pentagon 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 pentagons 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 pentagons count is A005891. See illustration. For n >= 1, (a(n) - a(n-1))/5 is A027383.
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LINKS
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Table of n, a(n) for n=0..37.
Kival Ngaokrajang, Illustration of initial terms
Index entries for linear recurrences with constant coefficients, signature (2,1,-4,2).
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FORMULA
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a(0) = 1, for n >= 1, a(n) = 5*A027383(n) + a(n-1).
a(n) = 2*a(n-1)+a(n-2)-4*a(n-3)+2*a(n-4). G.f.: -(2*x^3+3*x^2+4*x+1) / ((x-1)^2*(2*x^2-1)). - Colin Barker, Sep 21 2014
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PROG
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(PARI)
{
b=0; a=1; print1(1, ", ");
for (n=0, 50,
b=b+2^floor(n/2);
a=a+5*b;
print1(a, ", ")
)
}
(PARI)
Vec(-(2*x^3+3*x^2+4*x+1)/((x-1)^2*(2*x^2-1)) + O(x^100)) \\ Colin Barker, Sep 21 2014
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CROSSREFS
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Cf. A027383, A061777, A005891, A247618, A247620.
Sequence in context: A098943 A321973 A178465 * A120586 A171373 A048487
Adjacent sequences: A247616 A247617 A247618 * A247620 A247621 A247622
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KEYWORD
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nonn,easy
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AUTHOR
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Kival Ngaokrajang, Sep 21 2014
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EXTENSIONS
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More terms from Colin Barker, Sep 21 2014
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STATUS
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approved
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