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A143856
Ulam's spiral (ENE spoke).
4
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
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 *)
LinearRecurrence[{3, -3, 1}, {1, 12, 55}, 50] (* Harvey P. Dale, Sep 02 2024 *)
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
KEYWORD
nonn,easy
AUTHOR
STATUS
approved