A276123 a(0) = a(1) = a(2) = 1; for n > 2, a(n) = (a(n-1) + 1)*(a(n-2) + 1) / a(n-3).

1, 1, 1, 4, 10, 55, 154, 868, 2449, 13825, 39025, 220324, 621946, 3511351, 9912106, 55961284, 157971745, 891869185, 2517635809, 14213945668, 40124201194, 226531261495, 639469583290, 3610286238244, 10191389131441, 57538048550401, 162422756519761

Offset: 0

Author

Bruno Langlois, Aug 21 2016

Keywords

• nonn
• easy

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Matthew Christopher Russell, Using experimental mathematics to conjecture and prove theorems in the theory of partitions and commutative and non-commutative recurrences", PhD Dissertation, Mathematics Department, Rutgers University, May 2016.
• Index entries for linear recurrences with constant coefficients, signature (0,17,0,-17,0,1).

Crossrefs

Cf. A072881, A076839, A276175.

Programs

Magma

I:=[1,1,1,4,10,55]; [n le 6 select I[n] else 17*Self(n-2)-17*Self(n-4)+Self(n-6): n in [1..30]]; // Vincenzo Librandi, Aug 27 2016

Mathematica

LinearRecurrence[{0, 17, 0, -17, 0, 1}, {1, 1, 1, 4, 10, 55}, 40] (* Vincenzo Librandi, Aug 27 2016 *)
nxt[{a_,b_,c_}]:={b,c,((c+1)(b+1))/a}; NestList[nxt,{1,1,1},30][[All,1]] (* Harvey P. Dale, Oct 01 2021 *)

PARI

Vec((1+x-16*x^2-13*x^3+10*x^4+4*x^5)/((1-x)*(1+x)*(1-16*x^2+x^4)) + O(x^30)) \\ Colin Barker, Aug 21 2016

Formula

a(n) = (9-3*(-1)^n)/2*a(n-1) - a(n-2) - 1.

From Colin Barker, Aug 21 2016: (Start)

a(n) = 17*a(n-2) - 17*a(n-4) + a(n-6) for n > 5.

G.f.: (1 + x - 16*x^2 - 13*x^3 + 10*x^4 + 4*x^5) / ((1-x)*(1+x)*(1 - 16*x^2 + x^4)). (End)

a(2n+1) = A073352(n). a(2n) = A048907(n). - R. J. Mathar, Jul 04 2024

Extensions

More terms from Colin Barker, Aug 21 2016