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A082585 a(1)=1, a(n) = ceiling(r(5)*a(n-1)) where r(5) = (1/2)*(5 + sqrt(29)) is the positive root of X^2 = 5*X + 1. 0
1, 6, 32, 167, 868, 4508, 23409, 121554, 631180, 3277455, 17018456, 88369736, 458867137, 2382705422, 12372394248, 64244676663, 333595777564, 1732223564484, 8994713599985, 46705791564410, 242523671422036 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..21.

Index entries for linear recurrences with constant coefficients, signature (6,-4,-1).

FORMULA

For n > 3, a(n) = 6*a(n-1) - 4*a(n-2) - a(n-3); a(n) = floor(t(5)*r(5)^n) where t(5) = (1/10)*(1 + 7/sqrt(29)) is the positive root of 145*X^2 = 29*X + 1.

a(n) = -(1/5) + (3/5)*(5/2 + (1/2)*sqrt(29))^n + (16/145)*(5/2 + (1/2)*sqrt(29))^n*sqrt(29) + (3/5)*(5/2 - (1/2)*sqrt(29))^n - (16/145)*sqrt(29)*(5/2 - (1/2)*sqrt(29))^n, with n >= 0. - Paolo P. Lava, Jun 25 2008

G.f.: x/((x-1)*(x^2+5*x-1)). - Colin Barker, Jan 27 2013

G.f.: 1/(1/Q(0) + 3*x^3 - 3*x) where Q(k) = 1 + k*(2*x+1) + 8*x - 2*x*(k+1)*(k+5)/Q(k+1) ; (continued fraction). - Sergei N. Gladkovskii, Mar 15 2013

MAPLE

a:=n->sum(fibonacci(i, 5), i=0..n): seq(a(n), n=1..21); # Zerinvary Lajos, Mar 20 2008

MATHEMATICA

Join[{a=1, b=6}, Table[c=5*b+1*a+1; a=b; b=c, {n, 60}]] (* Vladimir Joseph Stephan Orlovsky, Feb 06 2011*)

LinearRecurrence[{6, -4, -1}, {1, 6, 32}, 30] (* Harvey P. Dale, Jan 06 2012 *)

CROSSREFS

Cf. A000071, A048739, A049652, A082574.

Sequence in context: A034942 A046714 A129171 * A084326 A199699 A306900

Adjacent sequences:  A082582 A082583 A082584 * A082586 A082587 A082588

KEYWORD

nonn,easy

AUTHOR

Benoit Cloitre, May 07 2003

STATUS

approved

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Last modified November 22 13:47 EST 2019. Contains 329393 sequences. (Running on oeis4.)