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A205646
Number of empty faces in Freij's family of Hansen polytopes.
2
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
OFFSET
0,1
COMMENTS
Freij's study produces a new family of Hansen polytopes that have only 3^d+16 nonempty faces.
LINKS
Ragnar Freij, Matthias Henze, Moritz W. Schmitt, and Günter M. Ziegler, Face numbers of centrally symmetric polytopes from split graphs, arXiv:1201.5790 [math.MG], 2012.
FORMULA
a(n) = 3^n + 16.
a(n) = 4*a(n-1) - 3*a(n-2). G.f.: (17 - 49*x) / ((1 - x)*(1 - 3*x)). - Colin Barker, May 02 2013
From Elmo R. Oliveira, Nov 09 2023: (Start)
a(n) = 3*a(n-1) - 32 with a(0) = 17.
E.g.f.: exp(3*x) + 16*exp(x). (End)
EXAMPLE
a(4) = (3^4) + 16 = 97.
MATHEMATICA
3^Range[0, 30]+16 (* Paolo Xausa, Oct 24 2023 *)
CROSSREFS
Cf. A000244 (powers of 3), A205647.
Sequence in context: A226684 A334287 A249566 * A281192 A073247 A133347
KEYWORD
nonn,easy
AUTHOR
Jonathan Vos Post, Jan 29 2012
EXTENSIONS
Terms corrected by Colin Barker, May 02 2013
STATUS
approved