1,2

a(n)/a(n-1) tends to 2.46750385...an eigenvalue of M and a root of the characteristic polynomial x^3 - x^2 - 2x - 4. A102001 is generated from [1 1 1 / 2 0 0 / 0 2 0] but has the same characteristic polynomial and recursive multipliers (1,2,4). A101000 uses the recursive multipliers (1,2,4,8).

a(n) = a(n-1) + 2*a(n-2) + 4*a(n-3), a>3. a(n) = center term in M^n * [1 1 1], where M = the 3X3 matrix [0 1 0 / 0 0 1 / 4 2 1]; M^n * [1 1 1] = [a(n-1) a(n) a(n+1)].

a(6) = 199 = 85 + 2*31 + 4*13 = a(5) + 2*a(4) + 4*a(3).

a(6) = 199 since M^6 * [1 1 1] = [85 199 493] = [a(5) a(6) a(7)].

sage: from sage.combinat.sloane_functions import recur_gen3 sage: it = recur_gen3(1, 1, 1, 1, 2, 4) sage: [it.next() for i in range(32)] - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 25 2008

Cf. A102000, A102001.

Sequence in context: A129781 A040061 A091432 this_sequence A053183 A102903 A026318

Adjacent sequences: A101999 A102000 A102001 this_sequence A102003 A102004 A102005

nonn

Gary W. Adamson (qntmpkt(AT)yahoo.com), Dec 23 2004