OFFSET
1,2
COMMENTS
If the "man or boy" program A(k, x1, x2, x3) from the program section is run with k > 0 and arbitrary x1, x2, and x3, the result is A055588(k-1)*x1 + A001519(k-1)*x2. - Eric M. Schmidt, Jun 24 2021
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..1000
K. Kuhapatanakul, On the Sums of Reciprocal Generalized Fibonacci Numbers, J. Int. Seq. 16 (2013) #13.7.1. See Theorem 3 p.3.
Index entries for linear recurrences with constant coefficients, signature (4,-4,1).
FORMULA
a(n) = 3*a(n-1) - a(n-2) - 1, n > 3. - Robert G. Wilson v, Apr 08 2004
G.f.: x - x^2*(2*x-1)*(x-2) / ( (x-1)*(x^2-3*x+1) ). - R. J. Mathar, Sep 06 2014
MATHEMATICA
a[1] = 1; a[2] = 2; a[n_] := a[n] = a[n - 1] + Sum[a[i] - a[1], {i, n - 1}]; Table[ a[n], {n, 30}]
Join[{1}, LinearRecurrence[{4, -4, 1}, {2, 3, 6}, 30]] (* Vincenzo Librandi, Feb 08 2017 *)
PROG
(PARI) a(n)=if(n==1, 1, if(n==2, 2, a(n-1)+sum(i=1, n-1, a(i)-a(1)))) \\ Edward Jiang, Sep 06 2014
(ALGOL-60) begin integer procedure A(k, x1, x2, x3);
value k; integer k;
integer x1, x2, x3;
begin integer procedure b;
begin
k:= k - 1;
B:= A := A (k, B, x1, x2);
end;
A := if k <= 0 then x2 + x3 else B;
end;
integer i;
for i:= 0 step 1 until 20 do
print (A (i, 1, 1, 0));
end
comment The above is a simplified Man or Boy Test program (cf. A132343), omitting the negative parameters from the original. - Leonid Broukhis, Feb 07 2017
(Magma) I:=[2, 3, 6]; [1] cat [n le 3 select I[n] else 4*Self(n-1)-4*Self(n-2)+Self(n-3): n in [1..30]]; // Vincenzo Librandi, Feb 08 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Amarnath Murthy, Apr 07 2004
EXTENSIONS
More terms from Robert G. Wilson v, Apr 08 2004
STATUS
approved