A270879 Expansion of (x+4*x^4)/(1-x-x^2-x^4-2*x^5-x^8).

0, 1, 1, 2, 7, 10, 20, 34, 65, 124, 230, 430, 800, 1494, 2792, 5210, 9727, 18155, 33892, 63271, 118110, 220484, 411588, 768337, 1434304, 2677500, 4998252, 9330536, 17417876, 32515004, 60697720, 113308101, 211519073, 394855430, 737100483, 1375989990

Offset

0,4

Links

Table of n, a(n) for n=0..35.

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

Formula

a(n) = n*Sum_{j=0..(n-1)/3} binomial(n-3*j,n-4*j)*F(n-3*j)/(n-3*j), where F(n) = A000045(n).

Mathematica

CoefficientList[Series[(x + 4 x^4)/(1 - x - x^2 - x^4 - 2 x^5 - x^8), {x, 0, 35}], x] (* Michael De Vlieger, Mar 28 2016 *)
LinearRecurrence[{1, 1, 0, 1, 2, 0, 0, 1}, {0, 1, 1, 2, 7, 10, 20, 34}, 40] (* Harvey P. Dale, Jul 03 2017 *)

Prog

(Maxima) a(n):=n*sum(binomial(n-3*j, n-4*j)/(n-3*j)*fib(n-3*j), j, 0, (n-1)/3); /* or */ taylor((x+4*x^4)/(1-x-x^2-x^4-2*x^5-x^8), x, 0, 10);
(PARI) a(n) = n*sum(k=0, (n-1)/3, binomial(n-3*k, n-4*k)/(n-3*k)*fibonacci(n-3*k)); \\ Altug Alkan, Mar 25 2016
(Magma) m:=40; R<x>:=PowerSeriesRing(Integers(), m); [0] cat Coefficients(R!((x+4*x^4)/(1-x-x^2-x^4-2*x^5-x^8)));

Crossrefs

Cf. A000045.

Sequence in context: A336903 A155171 A049830 * A022302 A345026 A023855

Adjacent sequences: A270876 A270877 A270878 * A270880 A270881 A270882

Keyword

nonn,easy

Author

Vladimir Kruchinin, Mar 25 2016

Status

approved