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A105693 a(n) = Fibonacci(2n+2)-2^n. 6
0, 1, 4, 13, 39, 112, 313, 859, 2328, 6253, 16687, 44320, 117297, 309619, 815656, 2145541, 5637351, 14799280, 38826025, 101809867, 266865720, 699311581, 1832117599, 4799138368, 12569491809, 32917725667, 86200462408, 225717215989, 591018294423, 1547471885008 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

REFERENCES

Czabarka, É., Flórez, R., Junes, L., & Ramírez, J. L. (2018). Enumerations of peaks and valleys on non-decreasing Dyck paths. Discrete Mathematics, 341(10), 2789-2807. See Table 4.

LINKS

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (5,-7,2).

FORMULA

G.f.: x(1-x)/((1-2x)(1-3x+x^2)); a(n)=sum{k=0..n+1, binomial(n+1, k+1)*sum{j=0..floor(k/2), F(k-2j)}}.

a(n) = A258109(n+1) + A001906(n), n>1. - Yuriy Sibirmovsky, Sep 12 2016

a(n) = 5*a(n-1)-7*a(n-2)+2*a(n-3) for n>2. - Colin Barker, Sep 12 2016

MATHEMATICA

Table[Fibonacci[2n+2]-2^n, {n, 0, 30}] (* or *) LinearRecurrence[{5, -7, 2}, {0, 1, 4}, 40] (* Harvey P. Dale, Jul 21 2016 *)

PROG

(MAGMA) [Fibonacci(2*n+2)-2^n: n in [0..30]]; // Vincenzo Librandi, Apr 21 2011

(PARI) concat(0, Vec(x*(1-x)/((1-2*x)*(1-3*x+x^2)) + O(x^40))) \\ Colin Barker, Sep 12 2016

(PARI) a(n)=fibonacci(2*n+2)-2^n \\ Charles R Greathouse IV, Sep 12 2016

CROSSREFS

Cf. A000045, A061667, A001906, A258109.

Sequence in context: A027076 A183112 A266429 * A215404 A290929 A121192

Adjacent sequences:  A105690 A105691 A105692 * A105694 A105695 A105696

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Apr 17 2005

STATUS

approved

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Last modified December 3 02:56 EST 2020. Contains 338899 sequences. (Running on oeis4.)