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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 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-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 Cf. A005891, A027383, A061777, A247618, A247620. See A358632 for a related concept. 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

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Last modified April 25 09:56 EDT 2024. Contains 371967 sequences. (Running on oeis4.)