A270737 a(n) = ((n+2)/2)*Sum_{k=0..n/2} (Sum_{i=0..n-2*k} (binomial(k+1,n-2*k-i)*binomial(k+i,k))*F(k+1)/(k+1)), where F(k) is Fibonacci numbers.

1, 3, 5, 10, 20, 42, 91, 195, 415, 880, 1864, 3952, 8385, 17795, 37765, 80138, 170044, 360810, 765595, 1624515, 3447071, 7314368, 15520400, 32932800, 69880225, 148279107, 314634021, 667623210, 1416632420, 3005958090, 6378354619

Offset

0,2

Links

Table of n, a(n) for n=0..30.

Index entries for linear recurrences with constant coefficients, signature (2, 0, 0, 0, 2, 1).

Formula

G.f.: (-x^2+x+1)/(-x^6-2*x^5-2*x+1).

a(n) = 2*a(n-1) + 2*a(n-5) + a(n-6). - G. C. Greubel, mar 25 2016

Mathematica

Table[((n + 2)/2) Sum[Sum[(Binomial[k + 1, n - 2 k - i] Binomial[k + i, k])/(k + 1) Fibonacci[k + 1], {i, 0, n - 2 k}], {k, 0, n/2}], {n, 0, 30}] (* or *)
CoefficientList[Series[(-x^2 + x + 1)/(-x^6 - 2 x^5 - 2 x + 1), {x, 0, 30}], x] (* Michael De Vlieger, Mar 25 2016 *)
LinearRecurrence[{2, 0, 0, 0, 2, 1}, {1, 3, 5, 10, 20, 42}, 100] (* G. C. Greubel, Mar 25 2016 *)

Prog

(Maxima)
a(n):=(n+2)/2*(sum(sum(binomial(k+1, n-2*k-i)*binomial(k+i, k), i, 0, n-2*k)*fib(k+1)/(k+1), k, 0, n/2));
(PARI) x='x+O('x^200); Vec((-x^2+x+1)/(-x^6-2*x^5-2*x+1)) \\ Altug Alkan, Mar 22 2016

Crossrefs

Cf. A000045, A113413.

Sequence in context: A158568 A068013 A342762 * A270724 A018104 A134365

Adjacent sequences: A270734 A270735 A270736 * A270738 A270739 A270740

Keyword

nonn

Author

Vladimir Kruchinin, Mar 22 2016

Status

approved