|
| |
|
|
A007204
|
|
Crystal ball sequence for D_4 lattice.
(Formerly M5182)
|
|
6
| |
|
|
1, 25, 169, 625, 1681, 3721, 7225, 12769, 21025, 32761, 48841, 70225, 97969, 133225, 177241, 231361, 297025, 375769, 469225, 579121, 707281, 855625, 1026169, 1221025
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,2
|
|
|
COMMENTS
| Equals binomial transform of [1, 24, 120, 192, 96, 0, 0, 0,...] [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Aug 13 2009]
Hypotenuse of Pythagorean triangles with hypotenuse a square: A057769(n)^2 + A069074(n-1)^2 = a(n)^2. -- [Martin Renner, Nov 12 2011]
|
|
|
REFERENCES
| Albert H. Beiler, Recreations in the theory of numbers, New York: Dover, (2nd ed.) 1966, p. 106, table 53.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
|
|
|
LINKS
| T. D. Noe, Table of n, a(n) for n=0..1000
J. H. Conway and N. J. A. Sloane, Low-Dimensional Lattices VII: Coordination Sequences, Proc. Royal Soc. London, A453 (1997), 2369-2389 (Abstract, pdf, ps).
Index entries for crystal ball sequences
Index entries for sequences related to D_4 lattice
|
|
|
FORMULA
| G.f.: (1+54*x^2+20*x+20*x^3+x^4)/(1-x)^5.
|
|
|
MAPLE
| (2*n^2+2*n+1)^2;
|
|
|
CROSSREFS
| Sequence in context: A198436 A080109 A017126 * A120096 A115330 A145964
Adjacent sequences: A007201 A007202 A007203 * A007205 A007206 A007207
|
|
|
KEYWORD
| nonn,easy,nice
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com) and J. H. Conway (conway(AT)math.princeton.edu)
|
| |
|
|
