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A171180 a(n) = (4n+1)^(1/2)/(4n+1) * ((1-p)q^n - (1-q)p^n) where p= (1-(4n+1)^(1/2))/2 and q = (1+(4n+1)^(1/2))/2 1
1, 3, 7, 29, 96, 463, 1905, 10233, 49159, 287891, 1557744, 9814741, 58451849, 392539575, 2532516511, 17999936497, 124360077816, 930257069563, 6822980957481, 53470578301581, 413527226164711, 3382254701784223, 27432377661111360, 233410016529114601 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

If s(n) is a sequence of the form s(0)=x, s(1)=x, s(n) = s(n-1) + k*s(n-2) then s(k) = a(n)*x. For example: if k=6 and x=3 s(6)=3,3,21,39,165,399,1389 =463*3.

REFERENCES

A. G. Shannon, J. V. Leyendekkers The Golden Ratio family and the Binet equation, Notes on Number Theory and Discrete Mathematics, Vol. 21, 2015, No. 2, 35-42.

LINKS

Table of n, a(n) for n=1..24.

FORMULA

a(n) = A193376(n,n). - Olivier Gérard, Jul 25 2011

a(n) = [x^n] 1/(1 - x - n*x^2). - Paul D. Hanna, Dec 27 2012

PROG

(PARI) {a(n)=polcoeff(1/(1-x-n*x^2+x*O(x^n)), n)} \\ Paul D. Hanna, Dec 27 2012

CROSSREFS

Sequence in context: A148765 A148766 A148767 * A151358 A110613 A088095

Adjacent sequences:  A171177 A171178 A171179 * A171181 A171182 A171183

KEYWORD

nonn

AUTHOR

Gary Detlefs, Dec 04 2009

STATUS

approved

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Last modified June 28 17:14 EDT 2017. Contains 288839 sequences.