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A279511 Sierpinski square-based pyramid numbers: a(n) = 5*a(n-1) - (2^(n+1)+7). 5
5, 14, 55, 252, 1221, 6034, 30035, 149912, 749041, 3744174, 18718815, 93589972, 467941661, 2339691914, 11698426795, 58492068432, 292460211081, 1462300793254, 7311503441975, 36557516161292, 182787578709301, 913937889352194, 4569689438372355, 22848447175084552 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Square pyramid where each face of the four triangular faces of the pyramid is a Sierpinski gasket. Similarly, a Sierpinski tetrahedron is sequence 4, 10, 34, 130, 514, 2050, 8194 (4^n*2)+2 (the double of A052539). The related octahedral form (creating tetrahedral openings), is A279512.

LINKS

Colin Barker, Table of n, a(n) for n = 0..1000

Wikipedia, Sierpinski triangle, see section "analogues in higher dimensions."

Eric Weisstein's World of Mathematics, Sierpinski Sieve.

Index entries for linear recurrences with constant coefficients, signature (8,-17,10).

FORMULA

a(n) = 5*a(n-1) - (2^(n+1)+7).

From Colin Barker, Dec 15 2016: (Start)

a(n) = 8*a(n-1) - 17*a(n-2) + 10*a(n-3) for n>2.

G.f.: (5-26*x+28*x^2) / ((1-x)*(1-2*x)*(1-5*x)).

(End)

MATHEMATICA

LinearRecurrence[{8, -17, 10}, {5, 14, 55}, 30] (* Harvey P. Dale, May 24 2017 *)

PROG

(PARI) Vec((5-26*x+28*x^2) / ((1-x)*(1-2*x)*(1-5*x)) + O(x^30)) \\ Colin Barker, Dec 15 2016

CROSSREFS

Cf. A000330, A047999, A279512.

Sequence in context: A177049 A127922 A262247 * A281698 A268814 A165517

Adjacent sequences:  A279508 A279509 A279510 * A279512 A279513 A279514

KEYWORD

nonn,easy,changed

AUTHOR

Steven Beard, Dec 13 2016

STATUS

approved

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Last modified May 25 14:22 EDT 2017. Contains 287038 sequences.