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

1, 2, 6, 36, 2048

Offset

1,2

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.

References

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

Links

Table of n, a(n) for n=1..5.

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.

Example

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.

Crossrefs

Cf. A008776, A020746, A010919, A010925.

Sequence in context: A152480 A001660 A368139 * A014052 A014056 A241300

Adjacent sequences: A275901 A275902 A275903 * A275905 A275906 A275907

Keyword

nonn,more

Author

N. J. A. Sloane, Aug 11 2016

Status

approved