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A082041
a(n) = 16*n^2 + 4*n + 1.
1
1, 21, 73, 157, 273, 421, 601, 813, 1057, 1333, 1641, 1981, 2353, 2757, 3193, 3661, 4161, 4693, 5257, 5853, 6481, 7141, 7833, 8557, 9313, 10101, 10921, 11773, 12657, 13573, 14521, 15501, 16513, 17557, 18633, 19741, 20881, 22053, 23257, 24493
OFFSET
0,2
COMMENTS
Also sequence found by reading the segment (1,21) together with the line from 21, in the direction 21, 73, ..., in the square spiral whose vertices are the generalized decagonal numbers A074377. - Omar E. Pol, Nov 02 2012
FORMULA
G.f.: (-1-18*x-13*x^2)/(x-1)^3 . - R. J. Mathar, Dec 03 2014
From Elmo R. Oliveira, Oct 28 2024: (Start)
E.g.f.: exp(x)*(1 + 20*x + 16*x^2).
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2. (End)
MATHEMATICA
Table[16n^2+4n+1, {n, 0, 50}] (* or *) LinearRecurrence[{3, -3, 1}, {1, 21, 73}, 50] (* Harvey P. Dale, Sep 28 2024 *)
PROG
(PARI) a(n)=16*n^2+4*n+1 \\ Charles R Greathouse IV, Jun 17 2017
CROSSREFS
Column k=4 of A082039.
Sequence in context: A240824 A109357 A283802 * A350160 A316887 A296155
KEYWORD
easy,nonn,changed
AUTHOR
Paul Barry, Apr 02 2003
STATUS
approved