OFFSET
2,2
COMMENTS
Fifth diagonal of array defined by T(i, 1)=T(1, j)=1, T(i, j)=Max(T(i-1, j)+T(i-1, j-1); T(i-1, j-1)+T(i, j-1)). - Benoit Cloitre, Aug 05 2003
LINKS
Index entries for linear recurrences with constant coefficients, signature (6,-13,13,-6,1).
FORMULA
G.f.: x^2/((1-3*x+x^2)*(1-x)^3).
a(n) = Sum_{k=0..n} binomial(n+2,k+3)*Fibonacci(k). - Vladimir Kruchinin, Oct 24 2016
a(n) = Sum_{k=0..n} binomial(k+1,2)*Fibonacci(2*n-2*k). - Greg Dresden and Yu Xiao, Jul 19 2020
MATHEMATICA
Rest[Rest[CoefficientList[Series[x^2/((1-3*x+x^2)*(1-x)^3), {x, 0, 27}], x]]] (* Georg Fischer, Apr 15 2020 *)
PROG
(Maxima) a(n):=sum(binomial(n+2, k+3)*fib(k), k, 0, n); /* Vladimir Kruchinin, Oct 24 2016 */
(Sage) [sum(binomial(k+1, 2)*fibonacci(2*n-2*k) for k in (0..n)) for n in (2..27)] # Stefano Spezia, Apr 24 2023
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, May 02 2000
STATUS
approved