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A123392 a(-3) = a(-2) = a(-1) = 0, a(0) = 1, a(n) = a(n-1) + 2*a(n-2) + 2*a(n-3) + a(n-4), for n>0. 7
0, 0, 0, 1, 1, 3, 7, 16, 37, 86, 199, 461, 1068, 2474, 5731, 13276, 30754, 71242, 165033, 382301, 885605, 2051515, 4752360, 11008901, 25502256, 59076293, 136850967, 317016966, 734373742, 1701185901, 3940818284, 9128954536, 21147336648 (list; graph; refs; listen; history; text; internal format)
OFFSET
-3,6
LINKS
FORMULA
a(n) = Sum_{k, 0<=k<=[n/2]} A016095(n-k,k).
G.f.: 1/(1-x-2*x^2-2*x^3-x^4).
a(n) = Sum_{k=0..n} C(n-k,k)*F(n-k+1). - Paul Barry, Mar 01 2010
MATHEMATICA
Join[{0, 0, 0}, CoefficientList[Series[1/(1 - x - 2*x^2 - 2*x^3 - x^4), {x, 0, 50}], x]] (* or *) Join[{0, 0, 0}, Table[Sum[ Binomial[n - k, k]*Fibonacci[n - k + 1], {k, 0, n}], {n, 0, 50}]] (* G. C. Greubel, Oct 13 2017 *)
LinearRecurrence[{1, 2, 2, 1}, {0, 0, 0, 1}, 40] (* Harvey P. Dale, Mar 01 2018 *)
PROG
(PARI) x='x+O('x^50); concat([0, 0, 0], Vec(1/(1-x-2*x^2-2*x^3-x^4))) \\ G. C. Greubel, Oct 13 2017
CROSSREFS
Sequence in context: A361507 A124671 A188626 * A095263 A010912 A192665
KEYWORD
nonn
AUTHOR
Philippe Deléham, Oct 14 2006
STATUS
approved

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Last modified August 30 00:57 EDT 2024. Contains 375520 sequences. (Running on oeis4.)