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A004116
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floor( (n^2 + 6n - 3)/4 ).
(Formerly M2524)
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5
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1, 3, 6, 9, 13, 17, 22, 27, 33, 39, 46, 53, 61, 69, 78, 87, 97, 107, 118, 129, 141, 153, 166, 179, 193, 207, 222, 237, 253, 269, 286, 303, 321, 339, 358, 377, 397, 417, 438, 459
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| a(n)-3 is the maximal size of a regular triangulation of a prism over a regular n-gon.
Solution to a postage stamp problem with 2 denominations.
This sequence is half the degree of the denominator of a certain sequence of rational polynomials defined in the referenced paper by G. Alkauskas. Although this fact is not documented in the paper it can be verified by running the authors code at http://www.alkauskas.puslapiai.lt/MP3/gkw.txt and evaluating degree(denom(...)) [From Stephen Crowley Sep 18, 2011]
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REFERENCES
| R. Alter and J. A. Barnett, A postage stamp problem, Amer. Math. Monthly, 87 (1980), 206-210.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 1..10000
G. Alkauskas, Recursive construction of a series converging to the eigenvalues of the Gauss-Kuzmin-Wirsing operator
M. Develin, Maximal triangulations of a regular prism
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 420
S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
Wikipedia, Gauss-Kuzmin-Wirsing operator
Index to sequences with linear recurrences with constant coefficients, signature (2,0,-2,1).
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FORMULA
| a(n)=floor((1/4)*n^2+(3/2)*n+1/4)-1
a(n)=(1/8)*(-1)^(n+1)-7/8+(3/2)*n+(1/4)*n^2
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MAPLE
| A004116:=(-1-z+z**3)/(z+1)/(z-1)**3; [Conjectured by S. Plouffe in his 1992 dissertation.]
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PROG
| (PARI) a(n)=(n^2+6*n-3)>>2
(MAGMA) [Floor( (n^2 + 6*n - 3)/4 ) : n in [1..50]]; // Vincenzo Librandi, Sep 19 2011
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CROSSREFS
| Sequence in context: A109512 A025205 A024190 * A004129 A171662 A004137
Adjacent sequences: A004113 A004114 A004115 * A004117 A004118 A004119
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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