OFFSET
1,3
COMMENTS
Numbers k such that k^2 - k is divisible by 16.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (1,1,-1).
FORMULA
a(n+1) = Sum_{k>=0} A030308(n,k)*b(k) with b(0)=1, b(k)=2^(k+3) for k > 0; {b(n)} = 1,16,32,64,128,256,... - Philippe Deléham, Oct 17 2011
G.f.: x^2*(1+15*x)/((1+x)*(1-x)^2). - Vincenzo Librandi, Jul 11 2012
a(n) = (32*n - 14*(-1)^n - 46)/4. - Vincenzo Librandi, Jul 11 2012
From David Lovler, Aug 18 2022: (Start)
a(n) = A321212(n) - 2.
a(n) = a(n-2) + 16.
E.g.f.: 15 + ((16*x - 23)*exp(x) - 7*exp(-x))/2. (End)
MATHEMATICA
CoefficientList[Series[x*(1+15*x)/((1+x)(1-x)^2), {x, 0, 60}], x] (* Vincenzo Librandi, Jul 11 2012 *)
LinearRecurrence[{1, 1, -1}, {0, 1, 16}, 80] (* Harvey P. Dale, Jul 24 2021 *)
PROG
(PARI) forstep(n=0, 200, [1, 15], print1(n", ")) \\ Charles R Greathouse IV, Oct 17 2011
(PARI) a(n) = (16*n - 7*(-1)^n - 23)/2 \\ David Lovler, Aug 18 2022
(Magma) [(32*n-14*(-1)^n-46)/4: n in [1..60]]; // Vincenzo Librandi, Jul 11 2012
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Aug 23 2009
STATUS
approved