OFFSET
0,2
COMMENTS
Binomial transform of the quasi-finite sequence 1,2,12,16,0,... (0 continued).
A bisection of A168582.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
FORMULA
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4).
G.f.: (1 - x + 11*x^2 + 5*x^3)/(x-1)^4.
First differences: a(n+1) - a(n) = 2*A054569(n+1).
Second differences: a(n+2) - 2*a(n+1) + a(n) = 4*A004767(n).
Third differences: a(n+3) - 3*a(n+2) + 3*a(n+1) - a(n) = 16.
a(n) = 1 - 2*n^2 + 4*A005900(n). - R. J. Mathar, Dec 05 2009
E.g.f.: (1/3)*(3 + 6*x + 18*x^2 + 8*x^3)*exp(x). - G. C. Greubel, Jul 26 2016
MATHEMATICA
Table[1-2*n^2+4*n*(1+2*n^2)/3, {n, 0, 50}] (* G. C. Greubel, Jul 26 2016 *)
LinearRecurrence[{4, -6, 4, -1}, {1, 3, 17, 59}, 60] (* Harvey P. Dale, May 21 2023 *)
PROG
(Magma) [1-2*n^2+4*n*(1+2*n^2)/3: n in [0..50] ]; // Vincenzo Librandi, Aug 06 2011
(PARI) a(n)=1-2*n^2+4*n*(1+2*n^2)/3 \\ Charles R Greathouse IV, Jul 26 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Paul Curtz, Nov 29 2009
EXTENSIONS
Edited and extended by R. J. Mathar, Dec 05 2009
STATUS
approved