A032795 - OEIS

%I #20 Sep 08 2022 08:44:51

%S 8,18,56,126,176,312,504,624,918,1292,1512,2024,2640,2990,3780,4698,

%T 5208,6336,7616,8316,9842,11544,12464,14448,16632,17802,20304,23030,

%U 24480,27560,30888,32648,36366,40356,42456,46872,51584,54054,59228

%N Positive numbers k such that (k+1)*(k+2)*(k+3)*(k+4)/(k+(k+1)+(k+2)+(k+3)+(k+4)) is an integer.

%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,3,-3,0,-3,3,0,1,-1).

%F a(n) = A032794(n)/A032793(n).

%F O.g.f.: 2*x*(4+5*x+19*x^2+23*x^3+10*x^4+11*x^5+3*x^6)/((1-x)^4* (1+x+x^2)^3). [Corrected by _Georg Fischer_, May 27 2019]

%t CoefficientList[Series[2*x*(4+5x+19x^2+23x^3+10x^4+11x^5+3x^6)/((1-x)^4*(1+x+x^2)^3), {x, 0, 39}], x] (* _Georg Fischer_, May 27 2019 *)

%o (PARI) Vec(2*x*(4+5*x+19*x^2+23*x^3+10*x^4+11*x^5+3*x^6)/((1-x)^4*(1+x+x^2)^3) + O(x^20)) \\ _Felix Fröhlich_, May 27 2019

%o (Magma) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( 2*x*(4+ 5*x +19*x^2+23*x^3+10*x^4+11*x^5+3*x^6)/((1-x)*(1-x^3)^3) )); // _G. C. Greubel_, May 29 2019

%o (Sage) a=(2*x*(4+ 5*x +19*x^2+23*x^3+10*x^4+11*x^5+3*x^6)/((1-x)*(1-x^3)^3) ).series(x, 30).coefficients(x, sparse=False); a[1:] # _G. C. Greubel_, May 29 2019

%Y Cf. A032793, A032794.

%K nonn,easy

%O 1,1

%A _Patrick De Geest_, May 15 1998

%E Definition amended and offset changed by _Georg Fischer_, May 27 2019