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A195315
Centered 32-gonal numbers.
7
1, 33, 97, 193, 321, 481, 673, 897, 1153, 1441, 1761, 2113, 2497, 2913, 3361, 3841, 4353, 4897, 5473, 6081, 6721, 7393, 8097, 8833, 9601, 10401, 11233, 12097, 12993, 13921, 14881, 15873, 16897, 17953, 19041, 20161, 21313, 22497, 23713, 24961, 26241
OFFSET
1,2
COMMENTS
Sequence found by reading the line from 1, in the direction 1, 33, ..., in the square spiral whose vertices are the generalized decagonal numbers A074377. Semi-axis opposite to A016802 in the same spiral.
FORMULA
a(n) = 16*n^2 - 16*n + 1.
G.f.: -x*(1 + 30*x + x^2) / (x-1)^3. - R. J. Mathar, Sep 18 2011
Sum_{n>=1} 1/a(n) = Pi*tan(sqrt(3)*Pi/4)/(8*sqrt(3)). - Amiram Eldar, Feb 11 2022
MATHEMATICA
Table[16*n^2 - 16*n + 1, {n, 1, 41}] (* Amiram Eldar, Feb 11 2022 *)
LinearRecurrence[{3, -3, 1}, {1, 33, 97}, 50] (* Harvey P. Dale, Feb 11 2024 *)
PROG
(Magma) [(16*n^2-16*n+1): n in [1..50]]; // Vincenzo Librandi, Sep 19 2011
(PARI) a(n)=16*n^2-16*n+1 \\ Charles R Greathouse IV, Oct 07 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Omar E. Pol, Sep 16 2011
STATUS
approved