

A247619


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


11



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

0,2


COMMENTS

Inspired by A061777, let us assign the label "1" to an origin pentagon; at the nth generation add a pentagon at each expandable vertex, i.e., a vertex such that the new added generations will not overlap existing ones, but overlapping among new generations is allowed. Each nonoverlapping pentagon will have the same label value as its predecessor; for the overlapping ones, the label value will be sum of label values of predecessors. The pentagon count is A005891. See illustration. [Edited for grammar/style by Peter Munn, Jan 14 2023]


LINKS



FORMULA

a(0) = 1, for n >= 1, a(n) = 5*A027383(n1) + a(n1). [Offset corrected by Peter Munn, Apr 20 2023]
a(n) = 2*a(n1)+a(n2)4*a(n3)+2*a(n4). G.f.: (2*x^3+3*x^2+4*x+1) / ((x1)^2*(2*x^21)).  Colin Barker, Sep 21 2014


PROG

(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)/((x1)^2*(2*x^21)) + O(x^100)) \\ Colin Barker, Sep 21 2014


CROSSREFS



KEYWORD

nonn,easy


AUTHOR



EXTENSIONS



STATUS

approved



