A253852 a(n) = a(n-4) * (a(n-3) + a(n-1)) / a(n-3), with a(0) = a(1) = a(2) = a(3) = 1.

1, 1, 1, 1, 2, 3, 4, 3, 4, 6, 12, 12, 12, 12, 24, 36, 48, 36, 48, 72, 144, 144, 144, 144, 288, 432, 576, 432, 576, 864, 1728, 1728, 1728, 1728, 3456, 5184, 6912, 5184, 6912, 10368, 20736, 20736, 20736, 20736, 41472, 62208, 82944, 62208, 82944, 124416, 248832

Offset

0,5

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,12).

Formula

a(n) = 1 / a(3-n) for all n in Z.

a(n+10) = 12*a(n), a(n+7)*a(n) = a(n+5)*a(n+2), a(n+6)*a(n+5) = 12*a(n+1)*a(n) for all n in Z.

0 = a(n)*(+a(n+1) + a(n+3)) + a(n+1)*(-a(n+4)) for all n in Z.

a(n) = 12^floor(n/10)*((1+0^((n-4) mod 10)+2*0^((n-5) mod 10)+2*0^((n-7) mod 10)+3*0^((n-6) mod 10)+3*0^((n-8) mod 10)+5*0^((n-9) mod 10)) mod 10). - Wesley Ivan Hurt, Apr 28 2015

G.f.: -(6*x^9+4*x^8+3*x^7+4*x^6+3*x^5+2*x^4+x^3+x^2+x+1) / (12*x^10-1). - Colin Barker, Apr 28 2015

Example

G.f. = 1 + x + x^2 + x^3 + 2*x^4 + 3*x^5 + 4*x^6 + 3*x^7 + 4*x^8 + 6*x^9 + ...

Mathematica

a[n_] := a[n] = a[n - 4] (a[n - 3] + a[n - 1])/a[n - 3]; a[0] = a[1] = a[2] = a[3] = 1; Array[a, 50] (* or *)
LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 0, 0, 12}, {1, 1, 1, 2, 3, 4, 3, 4, 6, 12}, 50] (* or *)
CoefficientList[ Series[(6x^9 + 4x^8 + 3x^7 + 4x^6 + 3x^5 + 2x^4 + x^3 + x^2 + x + 1)/(1 - 12 x^10), {x, 0, 50}], x] (* Robert G. Wilson v, Apr 28 2015 *)

Prog

(PARI) {a(n) = my(q=n\10, r=n%10+1); 2^([0, 0, 0, 0, 1, 0, 2, 0, 2, 1][r]+2*q) * 3^([0, 0, 0, 0, 0, 1, 0, 1, 0, 1][r]+q)};
(PARI) Vec(-(6*x^9+4*x^8+3*x^7+4*x^6+3*x^5+2*x^4+x^3+x^2+x+1)/(12*x^10-1) + O(x^100)) \\ Colin Barker, Apr 28 2015
(Magma) I:=[1, 1, 1, 1, 2, 3, 4, 3, 4, 6]; [n le 10 select I[n] else 12*Self(n-10): n in [1..100]]; // Vincenzo Librandi, Apr 29 2015

Crossrefs

Sequence in context: A221356 A177329 A360379 * A103672 A309255 A375290

Adjacent sequences: A253849 A253850 A253851 * A253853 A253854 A253855

Keyword

nonn,easy

Author

Michael Somos, Jan 17 2015

Status

approved