OFFSET
0,2
COMMENTS
The old definition of this sequence was "Generalized polygonal numbers".
Column T(n,4) of A080853.
Sequence found by reading the line from 1, in the direction 1, 11, ..., in the square spiral whose vertices are the generalized pentagonal numbers A001318. - Omar E. Pol, Sep 08 2011
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
G.f.: (C(3,0) + (C(5,2) - 2)*x + C(3,2)*x^2)/(1-x)^3 = (1 + 8*x + 3*x^2)/(1-x)^3.
E.g.f.: (1 + 10*x + 6*x^2)*exp(x). - Vincenzo Librandi, Apr 29 2016
a(n) = C(4,0) + C(4,1)n + C(4,2)n^2.
a(n) = A186424(2*n).
a(n) = 12*n + a(n-1) - 2 with n > 0, a(0)=1. - Vincenzo Librandi, Aug 08 2010
a(n) = (n+1)^4 mod n^3 for n >= 7. - J. M. Bergot, Aug 14 2017
a(n) = (2*n+1)^2 + 2*n^2. - Robert FERREOL, Jan 13 2024
MATHEMATICA
Table[6 n^2 + 4 n + 1, {n, 0, 50}] (* Vincenzo Librandi, Apr 29 2016 *)
PROG
(PARI) a(n)=6*n^2+4*n+1 \\ Charles R Greathouse IV, Oct 07 2015
(Magma) [6*n^2+4*n+1: n in [0..50]]; // Vincenzo Librandi, Apr 29 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Paul Barry, Feb 23 2003
EXTENSIONS
Definition replaced with the closed form by Bruno Berselli, Dec 10 2012
STATUS
approved