A122574 a(1) = a(2) = 1, a(n) = -11*a(n-1) + a(n-2).

1, 1, -10, 111, -1231, 13652, -151403, 1679085, -18621338, 206513803, -2290273171, 25399518684, -281684978695, 3123934284329, -34644962106314, 384218517453783, -4261048654097927, 47255753712530980, -524074339491938707, 5812073488123856757, -64456882708854363034

Offset: 1

Author

Roger L. Bagula, Sep 17 2006

Keywords

• sign
• easy

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).

Crossrefs

Cf. A049666.

Programs

Magma

[n le 2 select 1 else -11*Self(n-1) +Self(n-2): n in [1..30]]; // G. C. Greubel, Oct 30 2024

Mathematica

LinearRecurrence[{-11,1},{1,1},30] (* Harvey P. Dale, Aug 11 2017 *)

SageMath

A122574=BinaryRecurrenceSequence(-11,1,1,1)
[A122574(n-1) for n in range(1,31)] # G. C. Greubel, Oct 30 2024

Formula

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

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

Extensions

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