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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 *)

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: A274974 A251142 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 February 20 08:10 EST 2018. Contains 299366 sequences. (Running on oeis4.)