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A247619 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.) 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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
Inspired by A061777, let us assign the label "1" to an origin pentagon; at the n-th 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(n-1) + a(n-1). [Offset corrected by Peter Munn, Apr 20 2023]
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
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)/((x-1)^2*(2*x^2-1)) + O(x^100)) \\ Colin Barker, Sep 21 2014
CROSSREFS
See A358632 for a related concept.
Sequence in context: A098943 A321973 A178465 * A120586 A171373 A048487
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 09:56 EDT 2024. Contains 371967 sequences. (Running on oeis4.)