OFFSET
0,4
COMMENTS
Diagonal sums of number triangle A113020.
LINKS
Matthew House, Table of n, a(n) for n = 0..6387
Index entries for linear recurrences with constant coefficients, signature (2,-2,1,1).
FORMULA
a(n) = 2*a(n-1) - 2*a(n-2) + a(n-3) + a(n-4);
a(n) = Sum_{k=0..floor(n/2)} Sum_{j=0..n-k} C(n-k, j)*C(0, j-k)*Fibonacci(j-2k);
a(n) = Sum_{k=0..floor(n/2)} (-1)^(k+1)*binomial(n-k, k)*Fibonacci(k).
MATHEMATICA
Table[Sum[(-1)^(k + 1) Binomial[n - k, k] Fibonacci@ k, {k, 0, Floor[n/2]}], {n, 0, 44}] (* Michael De Vlieger, Feb 13 2017 *)
LinearRecurrence[{2, -2, 1, 1}, {0, 0, 1, 2}, 50] (* Harvey P. Dale, Jul 16 2018 *)
PROG
(PARI) a(n)=([0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1; 1, 1, -2, 2]^n*[0; 0; 1; 2])[1, 1] \\ Charles R Greathouse IV, Feb 14 2017
(PARI) x='x+O('x^30); concat([0, 0], Vec(x^2/(1-2*x+2*x^2-x^3-x^4))) \\ G. C. Greubel, Apr 09 2018
(Magma) I:=[0, 0, 1, 2]; [n le 4 select I[n] else 2*Self(n-1) - 2*Self(n-2) + Self(n-3) + Self(n-4): n in [1..30]]; // G. C. Greubel, Apr 09 2018
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Oct 11 2005
STATUS
approved