OFFSET
0,3
COMMENTS
According to the common formula for the polygonal numbers: (s-2)*n*(n-1)/2 + n (here s = 40).
The 4th number of the sequence, 117, is also the 10th pentagonal number (see A000326). The next number of the series, 232, is also the 9th decagonal number (see A001107), while 576 is the 25th square number (see A000290). The 12th number of the sequence, 2101, is the 23rd 11-gonal number (see A051682).
From Bruno Berselli, Aug 21 2015: (Start)
a(n) and a(n) - 2*n + 1 provide the numbers m such that 19*m + 81 is a square.
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
a(n) = n*(19*n - 18).
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3), for n > 2. - Colin Barker, Aug 11 2015
G.f.: -x*(37*x+1) / (x-1)^3. - Colin Barker, Aug 11 2015
E.g.f.: exp(x)*(x + 19*x^2). - Nikolaos Pantelidis, Feb 10 2023
MAPLE
MATHEMATICA
Table[n (19 n - 18), {n, 0, 45}] (* Bruno Berselli, Aug 21 2015 *)
PROG
(JavaScript) function a(n){return 38*n*(n-1)/2+n}
(PARI) concat(0, Vec(-x*(37*x+1)/(x-1)^3 + O(x^100))) \\ Colin Barker, Aug 11 2015
(PARI) first(m)=my(v=vector(m, i, i--; 38*i*(i-1)/2+i)); v; \\ Anders Hellström, Aug 13 2015
(Magma) [n*(19*n-18): n in [0..45]]; // Vincenzo Librandi, Aug 12 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Sergey Pavlov, Aug 11 2015
STATUS
approved