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Search: id:A005918
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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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+0
6
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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; listen)
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OFFSET
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0,2
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COMMENT
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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
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REFERENCES
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H. S. M. Coxeter, ``Polyhedral numbers,'' in R. S. Cohen et al., editors, For Dirk Struik. Reidel, Dordrecht, 1974, pp. 25-35.
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
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Milan Janjic, Two Enumerative Functions
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.
Cino Hilliard, 3n^2+2 not square.
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FORMULA
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G.f.: (1-x^2)*(1-x^3)/(1-x)^5.
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MAPLE
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A005918:=-(z+1)*(z**2+z+1)/(z-1)**3; [S. Plouffe in his 1992 dissertation.]
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PROGRAM
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(PARI) sq3nsqp2(n) = { for(x=1, n, y = 3*x*x+2; print1(y" ") ) }
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CROSSREFS
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Adjacent sequences: A005915 A005916 A005917 this_sequence A005919 A005920 A005921
Sequence in context: A005586 A031333 A047801 this_sequence A019262 A076042 A049791
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms from Cino Hilliard (hillcino368(AT)gmail.com), Mar 01 2003
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