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 A247620 Start with a single hexagon; at n-th generation add a hexagon at each expandable vertex; a(n) is the sum of all label values at n-th generation. (See comment for construction rules.) 10
 1, 7, 25, 67, 157, 343, 721, 1483, 3013, 6079, 12217, 24499, 49069, 98215, 196513, 393115, 786325, 1572751, 3145609, 6291331, 12582781, 25165687, 50331505, 100663147, 201326437, 402653023, 805306201, 1610612563, 3221225293, 6442450759, 12884901697 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Inspired by A061777, let us assign the label "1" to an origin hexagon; at n-th generation add a hexagon 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 squares 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 hexagons count is A003215. See llustration. For n >= 1, (a(n) - a(n-1))/6 is A000225 LINKS Table of n, a(n) for n=0..30. Kival Ngaokrajang, Illustration of initial terms Index entries for linear recurrences with constant coefficients, signature (4,-5,2). FORMULA a(0) = 1, for n >= 1, a(n) = 6*A000225(n) + a(n-1). From Colin Barker, Sep 21 2014: (Start) a(n) = (-11+3*2^(2+n)-6*n). a(n) = 4*a(n-1)-5*a(n-2)+2*a(n-3). G.f.: -(x+1)*(2*x+1) / ((x-1)^2*(2*x-1)). (End) PROG (PARI) a(n) = if (n<1, 1, 6*(2^n-1)+a(n-1)) for (n=0, 50, print1(a(n), ", ")) (PARI) Vec(-(x+1)*(2*x+1)/((x-1)^2*(2*x-1)) + O(x^100)) \\ Colin Barker, Sep 21 2014 CROSSREFS Cf. A000225, A061777, A003215, A247618, A247619. Sequence in context: A299262 A001296 A000970 * A240156 A155245 A155291 Adjacent sequences: A247617 A247618 A247619 * A247621 A247622 A247623 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 10:51 EDT 2024. Contains 371967 sequences. (Running on oeis4.)