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A026625 a(n) = Sum_{k=0..floor(n/2)} A026615(n-k,k). 1
1, 1, 2, 4, 7, 13, 21, 36, 58, 96, 155, 253, 409, 664, 1074, 1740, 2815, 4557, 7373, 11932, 19306, 31240, 50547, 81789, 132337, 214128, 346466, 560596, 907063, 1467661, 2374725, 3842388, 6217114, 10059504, 16276619, 26336125, 42612745, 68948872, 111561618 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

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

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

FORMULA

For n>1, a(n) = Fibonacci(n-1) + Lucas(n) - [3+(-1)^n]/2. - Ralf Stephan, May 13 2004

From Colin Barker, Jul 12 2017: (Start)

G.f.: (1 - x^2 + x^3 + x^4 + x^5) / ((1 - x)*(1 + x)*(1 - x - x^2)).

a(n) = 2^(-1-n)*(-5*((-2)^n + 3*2^n) - (-15+sqrt(5))*(1+sqrt(5))^n + (1-sqrt(5))^n*(15+sqrt(5))) / 5 for n>1.

a(n) = a(n-1) + 2*a(n-2) - a(n-3) - a(n-4) for n>5.

(End)

MATHEMATICA

Join[{1, 1}, Table[Fibonacci[n-1]+LucasL[n]-(3+(-1)^n)/2, {n, 2, 40}]] (* or *) Join[{1, 1}, LinearRecurrence[{1, 2, -1, -1}, {2, 4, 7, 13}, 40]] (* Harvey P. Dale, Sep 27 2011 *)

PROG

(PARI) Vec((1 - x^2 + x^3 + x^4 + x^5) / ((1 - x)*(1 + x)*(1 - x - x^2)) + O(x^50)) \\ Colin Barker, Jul 12 2017

CROSSREFS

Cf. A026615.

Sequence in context: A090752 A051058 A332578 * A026691 A018150 A019471

Adjacent sequences:  A026622 A026623 A026624 * A026626 A026627 A026628

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling

STATUS

approved

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Last modified January 23 16:13 EST 2022. Contains 350514 sequences. (Running on oeis4.)