A020872 Number of restricted forests in Moebius ladder M_n.

34, 241, 1582, 10204, 65197, 415076, 2638366, 16759249, 106427154, 675771276, 4290678337, 27242281044, 172964658642, 1098170541121, 6972388689086, 44268329738124, 281063582763949, 1784497634505876, 11329933410988622, 71934748718289089, 456720074988060962

Offset

2,1

Links

Peter J. Taylor, Table of n, a(n) for n = 2..500

Code Golf Stack Exchange, Counting the number of restricted forests on the Möbius ladder of length n

Peter Kagey, Example the a(2) = 34 restricted forests on M_2

J. P. McSorley, Counting structures in the Moebius ladder, Discrete Math., 184 (1998), 137-164.

Formula

For large n, (4.8820)^n < a(n) < (6.4188)^n (Th. 10.1.). - C. Ronaldo (aga_new_ac(AT)hotmail.com), Jan 17 2005

a(n) is asymptotic to c^n where c = 6.349088... is the inverse of the root of x^4 - x^3 - 4 x^2 + 7 x - 1 of smallest modulus. - Peter Kagey, May 10 2019

a(n) = 11*a(n-1) - 34*a(n-2) + 23*a(n-3) + 43*a(n-4) - 56*a(n-5) - 3*a(n-6) + 25*a(n-7) - 6*a(n-8) - 3*a(n-9) + a(n-10). - Peter J. Taylor, Mar 30 2019

G.f.: (4x^9 - 11x^8 - 31x^7 + 108x^6 - 264x^4 + 214x^3 + 87x^2 - 133x + 34)/(-x^10 + 3x^9 + 6x^8 - 25x^7 + 3x^6 + 56x^5 - 43x^4 - 23x^3 + 34x^2 - 11x + 1). - Peter Kagey, May 10 2019

Crossrefs

Sequence in context: A055716 A233300 A281052 * A302474 A183319 A190422

Adjacent sequences: A020869 A020870 A020871 * A020873 A020874 A020875

Keyword

nonn

Author

N. J. A. Sloane

Extensions

a(5)-a(12) from Peter J. Taylor, Mar 26 2019

a(13)-a(22) from Peter J. Taylor, Mar 30 2019

Status

approved