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A033816 a(n) = 2*n^2 + 3*n + 3. 20
3, 8, 17, 30, 47, 68, 93, 122, 155, 192, 233, 278, 327, 380, 437, 498, 563, 632, 705, 782, 863, 948, 1037, 1130, 1227, 1328, 1433, 1542, 1655, 1772, 1893, 2018, 2147, 2280, 2417, 2558, 2703, 2852, 3005, 3162, 3323, 3488, 3657, 3830, 4007, 4188, 4373, 4562 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
COMMENTS
For n >= 1, a(n) is the (1,1)-th entry in a (2*n+1) X (2*n+1) magic square built using the "north-east" technique. [Most probably the author is referring to the "Siamese method" described in the Wikipedia article. - Petros Hadjicostas, Jul 26 2020~]
LINKS
Guo-Niu Han, Enumeration of Standard Puzzles, 2011. [Cached copy]
Guo-Niu Han, Enumeration of Standard Puzzles, arXiv:2006.14070 [math.CO], 2020.
Wikipedia, Siamese method.
FORMULA
From Colin Barker, Jun 27 2012: (Start)
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
G.f.: (3 - x + 2*x^2)/(1 - x)^3. (End)
E.g.f.: (2*x^2 + 5*x + 3)*exp(x). - G. C. Greubel, Jul 15 2017
MATHEMATICA
a[n_]:=2*n^2+3*n+3; ...and/or...Array[ -#*(1-#*2)+2&, 5!, 0] (* Vladimir Joseph Stephan Orlovsky, Dec 21 2008 *)
CoefficientList[Series[(3-x+2*x^2)/(1-x)^3, {x, 0, 50}], x] (* Vincenzo Librandi, Jul 07 2012 *)
LinearRecurrence[{3, -3, 1}, {3, 8, 17}, 50] (* Harvey P. Dale, May 07 2015 *)
PROG
(Magma) I:=[3, 8, 17]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+Self(n-3): n in [1..50]]; // Vincenzo Librandi, Jul 07 2012
(PARI) a(n)=2*n^2+3*n+3 \\ Charles R Greathouse IV, Sep 24 2015
CROSSREFS
Sequence in context: A073433 A059518 A024929 * A011889 A188426 A349975
KEYWORD
easy,nonn
AUTHOR
Olivier Gorin (gorin(AT)roazhon.inra.fr)
EXTENSIONS
More terms from James A. Sellers, Jun 20 2000
Offset corrected by Charles R Greathouse IV, Jul 25 2010
STATUS
approved

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Last modified June 17 15:57 EDT 2024. Contains 373463 sequences. (Running on oeis4.)