

A080860


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
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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


LINKS

Table of n, a(n) for n=0..42.
Index entries for linear recurrences with constant coefficients, signature (3,3,1).


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)/(1x)^3 = (1+13*x+6*x^2)/(1x)^3
a(n) = 20*n+a(n1)5 with n>0, a(0)=1.  Vincenzo Librandi, Aug 08 2010


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 A297640
Adjacent sequences: A080857 A080858 A080859 * A080861 A080862 A080863


KEYWORD

nonn,easy


AUTHOR

Paul Barry, Feb 23 2003


EXTENSIONS

Definition replaced with the closed form by Bruno Berselli, Jan 16 2013


STATUS

approved



