cp's OEIS Frontend

A217775 a(n) = n*(n+1) + (n+2)*(n+3) + (n+4)*(n+5).

%I A217775 #24 Sep 08 2022 08:46:04
%S A217775 26,44,68,98,134,176,224,278,338,404,476,554,638,728,824,926,1034,
%T A217775 1148,1268,1394,1526,1664,1808,1958,2114,2276,2444,2618,2798,2984,
%U A217775 3176,3374,3578,3788,4004,4226,4454,4688,4928,5174,5426,5684,5948,6218,6494,6776,7064
%N A217775 a(n) = n*(n+1) + (n+2)*(n+3) + (n+4)*(n+5).
%H A217775 G. C. Greubel, <a href="/A217775/b217775.txt">Table of n, a(n) for n = 0..1000</a>
%H A217775 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A217775 G.f.: 2*(13-17*x+7*x^2)/(1-x)^3. - _Bruno Berselli_, Mar 29 2013
%F A217775 a(n) = 3*n^2 + 15*n + 26. - _Bruno Berselli_, Mar 29 2013
%F A217775 E.g.f.: (26 + 18*x + 3*x^2)*exp(x). - _G. C. Greubel_, Aug 27 2019
%F A217775 a(n) = 3*a(n-1)-3*a(n-2)+a(n-3). - _Wesley Ivan Hurt_, Jan 27 2022
%e A217775 a(1) = 1*2 + 3*4 + 5*6 = 2 + 12 + 30 = 44.
%p A217775 seq((3*(2*n+5)^2 + 29)/4, n=0..50); # _G. C. Greubel_, Aug 27 2019
%t A217775 Table[3n^2+15n+26,{n,0,50}] (* or *) LinearRecurrence[{3,-3,1}, {26,44,68}, 50] (* _Harvey P. Dale_, Oct 09 2018 *)
%o A217775 (JavaScript)
%o A217775 for (j=0;j<50;j++) {
%o A217775 a=j*(j+1)+(j+2)*(j+3)+(j+4)*(j+5);
%o A217775 document.write(a+", ");
%o A217775 }
%o A217775 (PARI) a(n)=n*(n+1)+(n+2)*(n+3)+(n+4)*(n+5) \\ _Charles R Greathouse IV_, Jun 17 2017
%o A217775 (Magma) [(3*(2*n+5)^2 + 29)/4: n in [0..50]]; // _G. C. Greubel_, Aug 27 2019
%o A217775 (Sage) [(3*(2*n+5)^2 + 29)/4 for n in (0..50)] # _G. C. Greubel_, Aug 27 2019
%o A217775 (GAP) List([0..50], n-> (3*(2*n+5)^2 + 29)/4 ); # _G. C. Greubel_, Aug 27 2019
%Y A217775 Cf. A051890 (two pairs), A217776 (4 pairs).
%K A217775 nonn,easy
%O A217775 0,1
%A A217775 _Jon Perry_, Mar 24 2013