1,2

a(n)/a(n-1) tends to 3.5133370916...; longest diagonal of the 11-gon given edge = 1, or (Sin 5*Pi/11)/(Sin Pi/11). Characteristic polynomial of M = x^5 - 3x^4 - 3x^3 + 4x^2 + x - 1.

a(n) = 3*a(n-1) + 3*a(n-2) - 4*a(n-3) - a(n-4) + a(n-5). Second column vector from left in M^n * [1,0,0,0,0], where M = the 5x5 matrix [1,1,1,1,1; 1,1,1,1,0; 1,1,1,0,0; 1,1,0,0,0; 1,0,0,0,0].

a(9) = 26703 = 3*a(8) + 3*a(7) - 4*a(6) - a(5) + a(4) = 3*7601 + 3*2163 - 4*616 - 175 + 50.

a(4)= 50 since M^4 * [1,0,0,0,0] = [55, 50, 41, 29, 15]; where a(4) = 50; and 55, 41, 29 and 15 are terms in the 5-wave sequence A038201.

Cf. A038201, A006358, A038342, A069006, A066170, A065941, A052963, A033304.

Sequence in context: A079309 A026630 A034459 this_sequence A055099 A047008 A047065

Adjacent sequences: A120744 A120745 A120746 this_sequence A120748 A120749 A120750

nonn,uned

Gary W. Adamson (qntmpkt(AT)yahoo.com), Jul 01 2006