login
A195048
Concentric 19-gonal numbers.
8
0, 1, 19, 39, 76, 115, 171, 229, 304, 381, 475, 571, 684, 799, 931, 1065, 1216, 1369, 1539, 1711, 1900, 2091, 2299, 2509, 2736, 2965, 3211, 3459, 3724, 3991, 4275, 4561, 4864, 5169, 5491, 5815, 6156, 6499, 6859, 7221, 7600, 7981, 8379, 8779, 9196
OFFSET
0,3
COMMENTS
Also concentric enneadecagonal numbers.
FORMULA
a(n) = (19/4)*n^2 + (15/8)*((-1)^n - 1).
From Colin Barker, Sep 16 2012: (Start)
a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4).
G.f.: x*(1 + 17*x + x^2)/((1-x)^3*(1+x)). (End)
Sum_{n>=1} 1/a(n) = Pi^2/114 + tan(sqrt(15/19)*Pi/2)*Pi/sqrt(285). - Amiram Eldar, Jan 17 2023
MATHEMATICA
LinearRecurrence[{2, 0, -2, 1}, {0, 1, 19, 39}, 50] (* Harvey P. Dale, May 17 2016 *)
PROG
(PARI) a(n)=19*n^2/4+15*((-1)^n-1)/8 \\ Charles R Greathouse IV, Oct 07 2015
CROSSREFS
Column 19 of A195040.
Sequence in context: A079044 A258016 A217731 * A299964 A041714 A041716
KEYWORD
nonn,easy
AUTHOR
Omar E. Pol, Sep 27 2011
STATUS
approved