A289433 Numbers c_n of Fibonacci-quilt legal decompositions of n.

1, 1, 1, 2, 2, 3, 4, 6, 9, 12, 17, 23, 32, 45, 63, 89, 124, 173, 241, 336, 470, 657, 919, 1284, 1793, 2504, 3497, 4886, 6827, 9539, 13327, 18617, 26007, 36331, 50756, 70910, 99066, 138400, 193348, 270111, 377352, 527174, 736484, 1028898, 1437409, 2008109, 2805394

Offset

1,4

Links

Table of n, a(n) for n=1..47.

Minerva Catral, P. L. Ford, P. E. Harris, S. J. Miller, et al., Legal Decompositions Arising from Non-positive Linear Recurrences, arXiv preprint arXiv:1606.09312 [math.CO], 2016.

Minerva Catral, Pari L. Ford, Pamela E. Harris, Steven J. Miller, and Dawn Nelson, Legal Decompositions Arising From Non-Positive Linear Recurrences, Fibonacci Quart. 54 (2016), no. 4, 348-365. See Table 1. p. 358.

Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,1,0,1).

Formula

Catral et al. give a linear recurrence.

G.f.: -(1+x)*(x^2-x+1)/(-1+x+x^5+x^7) . - R. J. Mathar, Aug 07 2017

Mathematica

LinearRecurrence[{1, 0, 0, 0, 1, 0, 1}, {1, 1, 1, 2, 2, 3, 4}, 50] (* Jean-François Alcover, Sep 14 2018 *)

Crossrefs

Cf. A289432.

Sequence in context: A186964 A005856 A157876 * A351973 A212264 A174650

Adjacent sequences: A289430 A289431 A289432 * A289434 A289435 A289436

Keyword

nonn

Author

N. J. A. Sloane, Jul 06 2017

Status

approved