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A190667 Expansion of (1+2*x)/(1-x^4-2*x^3-2*x^2-x). 0
1, 3, 5, 13, 30, 69, 160, 371, 859, 1990, 4610, 10679, 24738, 57306, 132750, 307517, 712367, 1650207, 3822725, 8855390, 20513621, 47520058, 110080805, 255003553, 590718900, 1368407674, 3169933385, 7343190086, 17010591104, 39405245720 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..29.

FORMULA

a(n) = (n+1)*sum(k=1..n+1, binomial(k, n-k+1)*A000045(k)/k).

a(n) = a(n-1)+2*a(n-2)+2*a(n-3)+a(n-4), a(0)=1, a(1)=3, a(2)=5, a(3)=13.

PROG

(Maxima) a(n):=(n+1)*sum(binomial(k, n-k+1)*fib(k)/k, k, 1, n+1); makelist(a(n), n, 0, 35);

(Maxima) a(n):=if n<0 then 0 else if n=0 then 1 else if n=1 then 3 else if n=2 then 5 else if n=3 then 13 else a(n-1)+2*a(n-2)+2*a(n-3)+a(n-4);

(MAGMA) [ (n+1)*&+[ (Binomial(k, n-k+1)*Fibonacci(k))/k: k in [1..n+1] ]: n in [0..35] ]; // Klaus Brockhaus, May 17 2011

(MAGMA) [ n eq 1 select 1 else n eq 2 select 3 else n eq 3 select 5 else n eq 4 select 13 else Self(n-1)+2*Self(n-2)+2*Self(n-3)+Self(n-4): n in [1..36] ]; // Klaus Brockhaus, Jun 01 2011

CROSSREFS

Sequence in context: A147046 A233232 A144471 * A062304 A281874 A135532

Adjacent sequences:  A190664 A190665 A190666 * A190668 A190669 A190670

KEYWORD

nonn

AUTHOR

Dmitry Kruchinin, May 16 2011

STATUS

approved

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Last modified September 20 22:20 EDT 2019. Contains 327252 sequences. (Running on oeis4.)