A297189 Expansion of (x + 3*x^2 - 2*x^3 - 3*x^4)/(1 - 8*x^2 + 9*x^4).

0, 1, 3, 6, 21, 39, 141, 258, 939, 1713, 6243, 11382, 41493, 75639, 275757, 502674, 1832619, 3340641, 12179139, 22201062, 80939541, 147542727, 537904077, 980532258, 3574776747, 6516373521, 23757077283, 43306197846, 157883627541, 287802221079

Offset: 0

Author

N. J. A. Sloane, Jan 04 2018, following a suggestion from Roger L. Bagula

Keywords

• nonn
• easy

Comments

Related to a tiling of the plane by heptagons.

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Peter Steinbach, Golden fields: a case for the heptagon, Math. Mag. Vol. 70, No. 1, Feb. 1997, 22-31.
• Index entries for linear recurrences with constant coefficients, signature (0,8,0,-9).

Programs

PARI

concat(0, Vec((x + 3*x^2 - 2*x^3 - 3*x^4)/(1 - 8*x^2 + 9*x^4) + O(x^40))) \\ Colin Barker, Jan 05 2018

Formula

a(n) = 8*a(n-2) - 9*a(n-4). - Colin Barker, Jan 05 2018

a(2*n)/a(2*n-1) ~ 2*a(2*n+1)/a(2*n) ~ 1 + sqrt(7). - Kyle MacLean Smith, Oct 11 2019