OFFSET
1,2
LINKS
Colin Barker, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (1,1,-1).
FORMULA
a(n) = 8*n-a(n-1)-11 (with a(1)=0). - Vincenzo Librandi, Aug 06 2010
a(n+1) = Sum_{k>=0} A030308(n,k)*b(k) with b(0)=5 and b(k)=2^(k+2) for k>0. - Philippe Deléham, Oct 17 2011
From Wesley Ivan Hurt, Mar 26 2015: (Start)
a(n) = a(n-1)+a(n-2)-a(n-3).
a(n) = (8n - 7 + (-1)^n)/2. (End)
G.f.: x^2*(5+3*x) / ((1-x)^2*(1+x)). - Colin Barker, Aug 25 2016
From Franck Maminirina Ramaharo, Jul 23 2018: (Start)
a(n) = A047470(n) - (-1)^(n - 1) + 1.
E.g.f.: (6 + exp(-x) + (8*x - 7)*exp(x))/2. (End)
Sum_{n>=2} (-1)^n/a(n) = log(2)/2 - (sqrt(2)-1)*Pi/16 - sqrt(2)*log(sqrt(2)+1)/8. - Amiram Eldar, Dec 18 2021
MAPLE
a:=n->add(4-(-1)^j, j=1..n): seq(a(n), n=0..59); # Zerinvary Lajos, Dec 13 2008
MATHEMATICA
Table[(8 n - 7 + (-1)^n)/2, {n, 1, 40}] (* Wesley Ivan Hurt, Mar 26 2015 *)
Rest@ CoefficientList[Series[x^2*(5 + 3 x)/((1 - x)^2*(1 + x)), {x, 0, 59}], x] (* Michael De Vlieger, Aug 25 2016 *)
Rest@(Range[0, 60]! CoefficientList[ Series[(6 + Exp[-x] + (8 x - 7)*Exp[x])/2, {x, 0, 60}], x]) (* or *)
LinearRecurrence[{1, 1, -1}, {0, 5, 8}, 60] (* Robert G. Wilson v, Jul 23 2018 *)
PROG
(PARI) forstep(n=0, 200, [5, 3], print1(n", ")) \\ Charles R Greathouse IV, Oct 17 2011
(PARI) concat(0, Vec(x^2*(5+3*x)/((1-x)^2*(1+x)) + O(x^100))) \\ Colin Barker, Aug 25 2016
(Magma) [(8*n - 7 + (-1)^n)/2 : n in [1..50]]; // Wesley Ivan Hurt, Mar 26 2015
(GAP) Filtered([0..250], n->n mod 8=0 or n mod 8=5); # Muniru A Asiru, Jul 23 2018
(Python)
def A047615(n): return (n<<2)-3-(n&1) # Chai Wah Wu, Mar 30 2024
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
More terms from Vincenzo Librandi, Aug 06 2010
STATUS
approved