A143860 Ulam's spiral (NNW spoke).

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

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

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

Adjacent sequences: A143857 A143858 A143859 * A143861 A143862 A143863

Keyword

nonn,easy

Author

Vladimir Joseph Stephan Orlovsky, Sep 03 2008

Status

approved