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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 Ragnar Freij, Matthias Henze, Moritz W. Schmitt, Günter 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.)