login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Please make a donation (tax deductible in USA) to keep the OEIS running. Over 5000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A106854 Expansion of 1/(1-x(1-5x)). 10
1, 1, -4, -9, 11, 56, 1, -279, -284, 1111, 2531, -3024, -15679, -559, 77836, 80631, -308549, -711704, 831041, 4389561, 234356, -21713449, -22885229, 85682016, 200108161, -228301919, -1228842724, -87333129, 6056880491, 6493546136, -23790856319, -56258586999, 62695694596, 343988629591 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Row sums of Riordan array (1,x(1-5x)). In general, a(n)=sum{k=0..n,(-1)^(n-k)*binomial(k,n-k)*r^(n-k)} yields the row sums of the Riordan array (1,x(1-kx)).

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..2859

Index entries for linear recurrences with constant coefficients, signature (1,-5).

FORMULA

a(n) = ((1+sqrt(-19))^(n+1)-(1-sqrt(-19))^(n+1))/(2^(n+1)sqrt(-19)).

a(n) = sum{k=0..n, (-1)^(n-k)*binomial(k, n-k)*5^(n-k)}.

a(n) = 5^(n/2)(cos(-n*acot(sqrt(19)/19))-sqrt(19)sin(-n*acot(sqrt(19)/19))/19).

a(n) = a(n-1)-5*a(n-2), a(0)=1, a(1)=1. [Philippe Deléham, Oct 21 2008]

a(n) = Sum_{k=0..n} A109466(n,k)*5^(n-k). [Philippe Deléham, Oct 25 2008]

G.f.: Q(0)/2, where Q(k) = 1 + 1/( 1 - x*(2*k+1 -5*x)/( x*(2*k+2 -5*x) + 1/Q(k+1) )); (continued fraction). - Sergei N. Gladkovskii, Dec 07 2013

MATHEMATICA

Join[{a=1, b=1}, Table[c=b-5*a; a=b; b=c, {n, 80}]] (* Vladimir Joseph Stephan Orlovsky, Jan 22 2011 *)

CoefficientList[Series[1/(1-x(1-5x)), {x, 0, 40}], x] (* or *) LinearRecurrence[ {1, -5}, {1, 1}, 40] (* Harvey P. Dale, Jan 21 2012 *)

PROG

(Sage) [lucas_number1(n, 1, 5) for n in xrange(1, 35)] # Zerinvary Lajos, Jul 16 2008

(PARI) Vec(1/(1-x+5*x^2) + O(x^99)) \\ Altug Alkan, Sep 06 2016

CROSSREFS

Cf. A106852, A106853, A145934.

Sequence in context: A277428 A002641 A085724 * A099458 A069219 A010413

Adjacent sequences:  A106851 A106852 A106853 * A106855 A106856 A106857

KEYWORD

easy,sign

AUTHOR

Paul Barry, May 08 2005

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified December 7 21:13 EST 2016. Contains 278895 sequences.