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A122574 a(1) = a(2) = 1, a(n) = -11a(n-1) + a(n-2). 2
1, 1, -10, 111, -1231, 13652, -151403, 1679085, -18621338, 206513803, -2290273171, 25399518684, -281684978695, 3123934284329, -34644962106314, 384218517453783, -4261048654097927, 47255753712530980, -524074339491938707, 5812073488123856757, -64456882708854363034 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Characteristic polynomial x^10+11*x^5-1 from the dodecahedral elliptic invariant j(x)=(x^20-228*x^15+494*x^10+228*x^5+1)^3/(-1728*x^5*(x^10+11*x^5-1)^5).

REFERENCES

Harry Hochstadt, The Functions of Mathematical Physics, Wiley, New York (1971), p. 170; also Dover, New York (1986),129-130

LINKS

Indranil Ghosh, Table of n, a(n) for n = 1..958

Tanya Khovanova, Recursive Sequences

Index entries for linear recurrences with constant coefficients, signature (-11,1).

FORMULA

|a(n)| = A049666(n-1)-A049666(n-2), n>1. [R. J. Mathar, Nov 02 2008]

G.f.: (x+12*x^2)/(1+11*x-x^2). [Philippe Deléham, Nov 20 2008]

a(n) = (13/50)*sqrt(5)*{[ -(11/2)+(5/2)*sqrt(5)]^(n-1)-[ -(11/2)-(5/2)*sqrt(5)]^(n-1)} +(1/2)*{[ -(11/2)+(5/2)*sqrt(5)]^(n-1)+[ -(11/2)-(5/2)*sqrt(5))^(n-1)}, with n>=1 [Paolo P. Lava, Feb 11 2009]

MATHEMATICA

a[0] = 1; a[1] = 1; a[2] = 1; a[3] = 1; a[4] = 1; a[5] = 1; a[6] = 1; a[7] = 1; a[8] = 1; a[9] = 1; a[n_] := a[n] = -11*a[n - 5] + a[n - 10] Table[a[5*n], {n, 0, 50}]

CROSSREFS

Sequence in context: A078252 A014993 A015592 * A176736 A084031 A210507

Adjacent sequences:  A122571 A122572 A122573 * A122575 A122576 A122577

KEYWORD

sign,easy

AUTHOR

Roger L. Bagula, Sep 17 2006

EXTENSIONS

Edited by N. J. A. Sloane, Dec 04 2006

STATUS

approved

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Last modified April 27 18:46 EDT 2017. Contains 285528 sequences.