OFFSET
1,2
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (4,-4,-2,4,0,-1).
FORMULA
From Andrew Howroyd, Aug 10 2018: (Start)
a(n) = n*(Fibonacci(n) - 1) + Sum_{k=1..n} Fibonacci(k).
a(n) = 4*a(n-1) - 4*a(n-2) - 2*a(n-3) + 4*a(n-4) - a(n-6).
G.f.: x*(1 - 2*x + 3*x^2 - 3*x^3)/((1 - x)^2*(1 - x - x^2)^2).
(End)
EXAMPLE
a(4) = 15 = sum of row 4, triangle A131411; (3 + 3 + 4 + 5).
MATHEMATICA
With[{F=Fibonacci}, Table[F[n+2]+n*F[n]-(n+1), {n, 40}]] (* G. C. Greubel, Jul 13 2019 *)
PROG
(PARI) a(n) = n*(fibonacci(n) - 1) + fibonacci(n+2) - 1; \\ Andrew Howroyd, Aug 10 2018
(PARI) Vec((1 - 2*x + 3*x^2 - 3*x^3)/((1 - x)^2*(1 - x - x^2)^2) + O(x^40)) \\ Andrew Howroyd, Aug 10 2018
(Magma) F:=Fibonacci; [F(n+2)+n*F(n)-(n+1): n in [1..40]]; // G. C. Greubel, Jul 13 2019
(Sage) f=fibonacci; [f(n+2)+n*f(n)-(n+1) for n in (1..40)] # G. C. Greubel, Jul 13 2019
(GAP) F:=Fibonacci;; List([1..40], n-> F(n+2)+n*F(n)-(n+1)); # G. C. Greubel, Jul 13 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Gary W. Adamson, Jul 08 2007
EXTENSIONS
Name changed and terms a(11) and beyond from Andrew Howroyd, Aug 10 2018
STATUS
approved