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 A289999 Sierpinski cuboctahedral numbers: a(n) = 16*4^n - 12*2^n + 9. 1
 13, 49, 217, 937, 3913, 16009, 64777, 260617, 1045513, 4188169, 16764937, 67084297, 268386313, 1073643529, 4294770697, 17179475977, 68718690313, 274876334089, 1099508482057, 4398040219657, 17592173461513, 70368719011849, 281474926379017, 1125899806179337, 4503599426043913, 18014398106828809 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Sierpinski cuboctahedron constructed by joining eight Sierpinski tetrahedra of sequence 4, 10, 34, 130, 514, 2050, 8194... (4^n*2)+2 (the double of A052539). This sequence is also Sierpinski recursion for the octahemioctahedron A274974. LINKS Colin Barker, Table of n, a(n) for n = 0..1000 Wikipedia, Sierpinski tetrahedron. Index entries for linear recurrences with constant coefficients, signature (7,-14,8). FORMULA a(n) = -3*2^(n + 2) + 2^(2n + 4) + 9. From Colin Barker, Sep 03 2017: (Start) G.f.: (13 - 42*x + 56*x^2) / ((1 - x)*(1 - 2*x)*(1 - 4*x)). a(n) = 7*a(n-1) - 14*a(n-2) + 8*a(n-3) for n>2. (End) MATHEMATICA CoefficientList[Series[(13 - 42 x + 56 x^2)/((1 - x) (1 - 2 x) (1 - 4 x)), {x, 0, 25}], x] (* Michael De Vlieger, Sep 03 2017 *) Table[16*4^n-12*2^n+9, {n, 0, 30}] (* or *) LinearRecurrence[{7, -14, 8}, {13, 49, 217}, 30] (* Harvey P. Dale, Dec 31 2018 *) PROG (PARI) Vec((13 - 42*x + 56*x^2) / ((1 - x)*(1 - 2*x)*(1 - 4*x)) + O(x^30)) \\ Colin Barker, Sep 03 2017 (PARI) a(n) = 16*4^n - 12*2^n + 9 \\ Charles R Greathouse IV, Nov 03 2017 CROSSREFS Cf. A005902, A290396, A274974, A281699, A067771, A279511. Sequence in context: A251142 A319086 A146287 * A147346 A147452 A146782 Adjacent sequences:  A289996 A289997 A289998 * A290000 A290001 A290002 KEYWORD nonn,easy AUTHOR Steven Beard, Sep 03 2017 STATUS approved

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Last modified January 22 14:24 EST 2019. Contains 319364 sequences. (Running on oeis4.)