

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 nth 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 nonoverlapping 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(n1))/5 is A027383.


LINKS

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).


FORMULA

a(0) = 1, for n >= 1, a(n) = 5*A027383(n) + a(n1).
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

Cf. A027383, A061777, A005891, A247618, A247620.
Sequence in context: A098943 A321973 A178465 * A120586 A171373 A048487
Adjacent sequences: A247616 A247617 A247618 * A247620 A247621 A247622


KEYWORD

nonn,easy


AUTHOR

Kival Ngaokrajang, Sep 21 2014


EXTENSIONS

More terms from Colin Barker, Sep 21 2014


STATUS

approved



