OFFSET
0,1
COMMENTS
Values of polynomial K_2 related to A090285: a(n) = K_2(n) = Sum_{k>=0} A090285(2,k)*2^k*binomial(n,k).
Numbers k such that 2*k+5 is a square. - Vincenzo Librandi, Oct 10 2013
a(n) is the area of a triangle with vertices at (b(n-2),b(n-1)), (b(n),b(n+1)), and (b(n+2),B(n+3)) for b(k)=A000292(k) with n>1. - J. M. Bergot, Mar 23 2017
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
a(n) = 2*A028387(n).
G.f.: 2*(1 +2*x -x^2)/(1-x)^3. - R. J. Mathar, Apr 02 2008
E.g.f.: 2*(1 +4*x +x^2)*exp(x). - G. C. Greubel, Jul 13 2017
Sum_{n>=0} 1/a(n) = 1/2 + Pi*tan(sqrt(5)*Pi/2)/(2*sqrt(5)). - Amiram Eldar, Dec 23 2022
MATHEMATICA
Table[2*(n^2 +3*n +1), {n, 0, 50}] (* Vincenzo Librandi, Oct 10 2013 *)
LinearRecurrence[{3, -3, 1}, {2, 10, 22}, 50] (* Harvey P. Dale, May 04 2017 *)
PROG
(PARI) a(n)=2*n^2+6*n+2 \\ Charles R Greathouse IV, Sep 24 2015
(Magma) [2*(1+3*n+n^2): n in [0..50]]; // G. C. Greubel, May 31 2019
(Sage) [2*(1+3*n+n^2) for n in (0..50)] # G. C. Greubel, May 31 2019
(GAP) List([0..50], n-> 2*(1+3*n+n^2)) # G. C. Greubel, May 31 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Philippe Deléham, Jan 25 2004
EXTENSIONS
Corrected by T. D. Noe, Nov 12 2006
STATUS
approved