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A205646 Number of empty faces in Freij's family of Hansen polytopes. 1
17, 19, 25, 43, 97, 259, 745, 2203, 6577, 19699, 59065, 177163, 531457, 1594339, 4782985, 14348923, 43046737, 129140179, 387420505, 1162261483, 3486784417, 10460353219, 31381059625, 94143178843, 282429536497, 847288609459, 2541865828345, 7625597485003 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Freij's study produces a new family of Hansen polytopes that have only 3^d+16 nonempty faces. The subsequence of primes begins with n = 0, 1, 3, 4, 7, 8, 9, 12, 13, 15, 27, 31, 49, ... A205647, giving  17, 19, 43, 97, 2203, 6577, 19699, 531457, 1594339, 14348923, 7625597485003, 239299329230617529590099.

LINKS

Table of n, a(n) for n=0..27.

Ragnar Freij, Matthias Henze, Moritz W. Schmitt, G√ľnter M. Ziegler, Face numbers of centrally symmetric polytopes from split graphs, arXiv:1201.5790v1 [math.MG], Jan 27, 2012.

Index entries for linear recurrences with constant coefficients, signature (4,-3).

FORMULA

a(n) = 3^n + 16.

a(n) = 4*a(n-1)-3*a(n-2). G.f.: -(49*x-17) / ((x-1)*(3*x-1)). - Colin Barker, May 02 2013

EXAMPLE

a(4) = (3^4) + 16 = 97.

CROSSREFS

Cf. A000244 Powers of 3, A205647.

Sequence in context: A226684 A334287 A249566 * A281192 A073247 A133347

Adjacent sequences:  A205643 A205644 A205645 * A205647 A205648 A205649

KEYWORD

nonn,easy

AUTHOR

Jonathan Vos Post, Jan 29 2012

EXTENSIONS

Terms corrected by Colin Barker, May 02 2013

STATUS

approved

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Last modified September 28 08:33 EDT 2020. Contains 337394 sequences. (Running on oeis4.)