A143856 Ulam's spiral (ENE spoke).

1, 12, 55, 130, 237, 376, 547, 750, 985, 1252, 1551, 1882, 2245, 2640, 3067, 3526, 4017, 4540, 5095, 5682, 6301, 6952, 7635, 8350, 9097, 9876, 10687, 11530, 12405, 13312, 14251, 15222, 16225, 17260, 18327, 19426, 20557, 21720, 22915, 24142

Offset

1,2

Comments

Also sequence found by reading the segment (1, 12) together with the line from 12, in the direction 12, 55,..., 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 - 37*n + 22. - R. J. Mathar, Sep 08 2008

G.f. x*(1 + 9*x + 22*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.: -22 + (22 - 21*x + 16*x^2)*exp(x). - G. C. Greubel, Nov 09 2019

Maple

seq( ((32*n-37)^2 +39)/64, n=1..40); # G. C. Greubel, Nov 09 2019

Mathematica

f[n_]:= 16n^2 -37n +22; Array[f, 40] (* Robert G. Wilson v, Oct 31 2011 *)
Table[16n^2-37*n+22, {n, 1, 40}] (* Vincenzo Librandi, Jul 10 2012 *)

Prog

(Magma) [16*n^2 -37*n +22: n in [1..40]]; // Vincenzo Librandi, Jul 10 2012
(PARI) a(n)=16*n^2-37*n+22 \\ Charles R Greathouse IV, Jun 17 2017
(Sage) [((32*n-37)^2 +39)/64 for n in (1..40)] # G. C. Greubel, Nov 09 2019
(GAP) List([1..40], n-> ((32*n-37)^2 +39)/64); # G. C. Greubel, Nov 09 2019

Crossrefs

Sequence in context: A230920 A190948 A275249 * A207102 A343539 A229424

Adjacent sequences: A143853 A143854 A143855 * A143857 A143858 A143859

Keyword

nonn,easy

Author

Vladimir Joseph Stephan Orlovsky, Sep 03 2008

Status

approved