A275904 Order of homogeneous linear recurrence satisfied by the Pisot sequence T(n, n^2-n+1).

1, 2, 6, 36, 2048

Offset: 1

Author

N. J. A. Sloane, Aug 11 2016

Keywords

• nonn
• more

Comments

Degree of denominator of minimal g.f. for T(n, n^2-n+1).

Conjecture: a(6) = 6852224. The conjectured generating function for T(6,31) is A(x)/(1+x - x*A(x)) where A(x) = 6 + x - x^2 - x^4 - x^22 - x^1130 - x^6852224 (and as usual there is a common factor of (1+x) in numerator and denominator). - David Boyd, Aug 12 2016.

Examples

			T(1,1) is the all-ones sequence, with g.f. 1/(1-x).
T(2,3) is 2,3,4,5,6,... with g.f. (2-x)/(1-2*x+x^2).
T(3,7) is A020746, with a linear recurrence of order 6.
T(4,13) is A010919, with a linear recurrence of order 36.
T(5,21) is A010925, with a linear recurrence of order 2048.
		

References

• David Boyd, Email communication to N. J. A. Sloane, Aug 06 2016

Links

• D. W. Boyd, Pisot sequences which satisfy no linear recurrences, Acta Arith. 32 (1) (1977) 89-98
• D. W. Boyd, Some integer sequences related to the Pisot sequences, Acta Arithmetica, 34 (1979), 295-305
• D. W. Boyd, On linear recurrence relations satisfied by Pisot sequences, Acta Arithm. 47 (1) (1986) 13
• D. W. Boyd, Pisot sequences which satisfy no linear recurrences. II, Acta Arithm. 48 (1987) 191
• D. W. Boyd, Linear recurrence relations for some generalized Pisot sequences, in Advances in Number Theory (Kingston ON, 1991), pp. 333-340, Oxford Univ. Press, New York, 1993; with updates from 1996 and 1999.

Crossrefs

Cf. A008776, A020746, A010919, A010925.