A367806 - OEIS

%I #23 Jan 10 2024 04:56:37

%S 0,1,3,4,6,2,9,10,12,5,15,16,18,7,21,22,24,8,27,28,30,11,33,34,36,13,

%T 39,40,42,14,45,46,48,17,51,52,54,19,57,58,60,20,63,64,66,23,69,70,72,

%U 25,75,76,78,26,81,82,84,29,87,88,90,31,93,94,96,32,99

%N Inverse permutation of A160080.

%C Permutation of nonnegative numbers.

%H <a href="/index/Rec#order_16">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,-1).

%F a(2*n) = 3*n = A008585(n).

%F a(4*n+3) = 6*n+4 = A016957(n).

%F a(4*n+1) = A047268(n+1).

%F a(n) = a(n-4) + a(n-12) - a(n-16).

%F G.f.: (x + 3*x^2 + 4*x^3 + 6*x^4 + x^5 + 6*x^6 + 6*x^7 + 6*x^8 + 3*x^9 + 6*x^10 + 6*x^11 + 6*x^12 + x^13 + 3*x^14 + 2*x^15) / ((1 - x^4)*(1 - x^12)).

%e As an array of four columns read by rows, the columns are A008588, A047268, A016945, A016957:

%e    0,  1,  3,  4;

%e    6,  2,  9, 10;

%e   12,  5, 15, 16;

%e   18,  7, 21, 22;

%e   24,  8, 27, 28;

%e   30, 11, 33, 34;

%e   ...

%t CoefficientList[Series[(x + 3*x^2 + 4*x^3 + 6*x^4 + x^5 + 6*x^6 + 6*x^7 + 6*x^8 + 3*x^9 + 6*x^10 + 6*x^11 + 6*x^12 + x^13 + 3*x^14 + 2*x^15) / ((1-x)^2*(1+x)*(1+x^2)*(1+x+x^2)*(1+x^3)*(1+x^6)),{x,0,66}],x] (* _Stefano Spezia_, Dec 27 2023 *)

%Y Cf. A008585, A008588, A016945, A016957, A047268, A160080.

%K nonn,easy,tabf

%O 0,3

%A _Philippe Deléham_, Dec 01 2023