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A005918
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Number of points on surface of square pyramid: 3*n^2 + 2 (n>0).
(Formerly M3843)
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10
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1, 5, 14, 29, 50, 77, 110, 149, 194, 245, 302, 365, 434, 509, 590, 677, 770, 869, 974, 1085, 1202, 1325, 1454, 1589, 1730, 1877, 2030, 2189, 2354, 2525, 2702, 2885, 3074, 3269, 3470, 3677, 3890, 4109, 4334, 4565, 4802, 5045, 5294, 5549, 5810, 6077, 6350, 6629
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Also coordination sequence of the 5-connected net = hexagonal net X integers.
Also (except for initial term) numbers of the form 3n^2+2 that are not squares. See link for proof. - Cino Hilliard (hillcino368(AT)gmail.com), Mar 01 2003
If a 2-set Y and a 3-set Z are disjoint subsets of an n-set X then a(n-4) is the number of 4-subsets of X intersecting both Y and Z. - Milan R. Janjic (agnus(AT)blic.net), Sep 08 2007
Sums of three consecutive squares: (n-2)^2+(n-1)^2+n^2 for n>1 [From Keith D. Tyler (oeis(AT)keithtyler.com), Aug 10 2010]
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REFERENCES
| H. S. M. Coxeter, ``Polyhedral numbers,'' in R. S. Cohen et al., editors, For Dirk Struik. Reidel, Dordrecht, 1974, pp. 25-35.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
B. K. Teo and N. J. A. Sloane, Magic numbers in polygonal and polyhedral clusters, Inorgan. Chem. 24 (1985), 4545-4558.
A. F. Wells, Three-Dimensional Nets and Polyhedra, Fig. 15.1 (e).
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LINKS
| Milan Janjic, Two Enumerative Functions
Cino Hilliard, 3n^2+2 not square.
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.
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FORMULA
| G.f.: (1-x^2)*(1-x^3)/(1-x)^5.
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MAPLE
| A005918:=-(z+1)*(z**2+z+1)/(z-1)**3; [S. Plouffe in his 1992 dissertation.]
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MATHEMATICA
| Differences[LisT_]:=(Drop[LisT, 2]-Drop[LisT, -2]+2)/2; Differences[Range[0, 5! ]^3] [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Feb 07 2010]
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PROG
| (PARI) sq3nsqp2(n) = { for(x=1, n, y = 3*x*x+2; print1(y" ") ) }
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CROSSREFS
| Cf. A206399.
Sequence in context: A031333 A161437 A047801 * A019262 A076042 A162208
Adjacent sequences: A005915 A005916 A005917 * A005919 A005920 A005921
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KEYWORD
| nonn,easy,changed
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Cino Hilliard (hillcino368(AT)gmail.com), Mar 01 2003
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