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A143860
Ulam's spiral (NNW spoke).
4
1, 16, 63, 142, 253, 396, 571, 778, 1017, 1288, 1591, 1926, 2293, 2692, 3123, 3586, 4081, 4608, 5167, 5758, 6381, 7036, 7723, 8442, 9193, 9976, 10791, 11638, 12517, 13428, 14371, 15346, 16353, 17392, 18463, 19566, 20701, 21868, 23067, 24298
OFFSET
1,2
COMMENTS
Also, except for the first term, sequence found by reading the line from 16, in the direction 16, 63,... in the square spiral whose vertices are the generalized decagonal numbers A074377. - Omar E. Pol, Nov 05 2012
FORMULA
a(n) = 16*n^2 - 33*n + 18. - R. J. Mathar, Sep 08 2008
G.f. x*(1 + 13*x + 18*x^2)/(1-x)^3. - R. J. Mathar, Oct 31 2011
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Vincenzo Librandi, Jul 10 2012
E.g.f.: -18 + (18 - 17*x + 16*x^2)*exp(x). - G. C. Greubel, Nov 09 2019
MAPLE
seq( ((32*n-33)^2 +63)/64, n=1..40); # G. C. Greubel, Nov 09 2019
MATHEMATICA
f[n_]:= 16n^2 -33n +18; Array[f, 40] (* Robert G. Wilson v, Oct 31 2011 *)
((32*Range[50]-33)^2 +63)/64 (* G. C. Greubel, Nov 09 2019 *)
PROG
(Magma) [16*n^2-33*n+18: n in [1..40]]; // Vincenzo Librandi, Jul 10 2012
(PARI) a(n)=16*n^2-33*n+18 \\ Charles R Greathouse IV, Jun 17 2017
(Sage) [((32*n-33)^2 +63)/64 for n in (1..40)] # G. C. Greubel, Nov 09 2019
(GAP) List([1..40], n-> ((32*n-33)^2 +63)/64); # G. C. Greubel, Nov 09 2019
CROSSREFS
Sequence in context: A356249 A066391 A022289 * A100176 A060091 A076751
KEYWORD
nonn,easy
AUTHOR
STATUS
approved