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A080860
a(n) = 10*n^2 + 5*n + 1.
1
1, 16, 51, 106, 181, 276, 391, 526, 681, 856, 1051, 1266, 1501, 1756, 2031, 2326, 2641, 2976, 3331, 3706, 4101, 4516, 4951, 5406, 5881, 6376, 6891, 7426, 7981, 8556, 9151, 9766, 10401, 11056, 11731, 12426, 13141, 13876, 14631, 15406, 16201, 17016, 17851
OFFSET
0,2
COMMENTS
The old definition of this sequence was "Generalized polygonal numbers".
Column T(n,5) of A080853.
Sequence found by reading the line from 1, in the direction 1, 16, ..., in the square spiral whose vertices are the generalized heptagonal numbers A085787. - Omar E. Pol, Sep 10 2011
FORMULA
a(n) = C(5,0) + C(5,1)*n + C(5,2)*n^2.
G.f.: (C(4,0) + (C(6,2) - 2)*x + C(4,2)*x^2)/(1-x)^3 = (1 + 13*x + 6*x^2)/(1-x)^3.
a(n) = 20*n + a(n-1) - 5 with n > 0, a(0)=1. - Vincenzo Librandi, Aug 08 2010
From Elmo R. Oliveira, Oct 31 2024: (Start)
E.g.f.: exp(x)*(1 + 15*x + 10*x^2).
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2. (End)
MATHEMATICA
Table[10n^2+5n+1, {n, 0, 50}] (* or *) LinearRecurrence[{3, -3, 1}, {1, 16, 51}, 50] (* Harvey P. Dale, Aug 05 2014 *)
PROG
(PARI) a(n)=10*n^2+5*n+1 \\ Charles R Greathouse IV, Jun 17 2017
CROSSREFS
Sequence in context: A221485 A204723 A204962 * A204716 A192248 A363350
KEYWORD
nonn,easy,changed
AUTHOR
Paul Barry, Feb 23 2003
EXTENSIONS
Definition replaced with the closed form by Bruno Berselli, Jan 16 2013
STATUS
approved