A138747 a(n) = 4*a(n-1) - 3*a(n-2) + 2*a(n-3) - 1*a(n-4).

1, 1, 1, 2, 6, 19, 61, 197, 637, 2060, 6662, 21545, 69677, 225337, 728745, 2356778, 7621874, 24649315, 79716449, 257804821, 833746693, 2696355892, 8720076682, 28200927617, 91202445513, 294950796673, 953877628705, 3084862088210, 9976514614558, 32264276654339, 104343409321397, 337448974463477, 1091317708583837, 3529346452933372, 11413987225587534

Offset

1,4

Comments

a(n)/a(n-1) tends to 3.2340228928..., an eigenvalue of the matrix X and a root to x^4 - 4*x^3 + 3*x^2 - 2*x + 1 = 0.

Links

Table of n, a(n) for n=1..35.

Formula

a(n) = 4*a(n-1) - 3*a(n-2) + 2*a(n-3) - 1*a(n-4); a>4. Let X = the 4 X 4 matrix [0,1,0,0; 0,0,1,0; 0,0,0,1; -1,2,-3,4]. X^n * [1,1,1,1] = [a(n), a(n+1), a(n+2), a(n+3)].

O.g.f.: -x(-1+3x+x^3)/(1-4x+3x^2-2x^3+x^4). - R. J. Mathar, Apr 03 2008

Example

a(7) = 61 = 4*a(6) - 3*a(5) + 2*a(4) - 1*a(3) = 4*19 - 3*6 + 2*2 - 1*1.
X^4 * [1,1,1,1] = [a(4), a(5), a(6), a(7)] = [2, 6, 19, 61].

Crossrefs

Sequence in context: A018906 A014010 A022015 * A052975 A275943 A228180

Adjacent sequences: A138744 A138745 A138746 * A138748 A138749 A138750

Keyword

nonn

Author

Gary W. Adamson, Mar 28 2008

Extensions

More terms from R. J. Mathar, Apr 03 2008

Status

approved