A218471 - OEIS

%I #31 Nov 01 2024 02:00:31

%S 0,2,11,27,50,80,117,161,212,270,335,407,486,572,665,765,872,986,1107,

%T 1235,1370,1512,1661,1817,1980,2150,2327,2511,2702,2900,3105,3317,

%U 3536,3762,3995,4235,4482,4736,4997,5265,5540,5822,6111,6407,6710,7020,7337

%N a(n) = n*(7*n-3)/2.

%H G. C. Greubel, <a href="/A218471/b218471.txt">Table of n, a(n) for n = 0..5000</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).

%F G.f.: x*(2+5*x)/(1-x)^3.

%F a(n) = 3*a(n-1) -3*a(n-2) +a(n-3) with a(0)=0, a(1)=2, a(2)=11.

%F a(n) = A001106(n) +  n.

%F a(n) = A022264(n) -  n.

%F a(n) = A022265(n) - 2*n.

%F a(n) = A186029(n) - 3*n.

%F a(n) = A179986(n) - 4*n.

%F a(n) = A024966(n) - 5*n.

%F a(n) = A174738(7*n+1).

%F E.g.f.: (x/2)*(7*x + 4)*exp(x). - _G. C. Greubel_, Aug 23 2017

%p seq(n*(7*n-3)/2, n=0..50); # _G. C. Greubel_, Aug 31 2019

%t Table[n*(7*n-3)/2, {n,0,50}] (* _G. C. Greubel_, Aug 23 2017 *)

%o (PARI) a(n)=n*(7*n-3)/2 \\ _Charles R Greathouse IV_, Jun 17 2017

%o (Magma) [n*(7*n-3)/2: n in [0..50]]; // _G. C. Greubel_, Aug 31 2019

%o (Sage) [n*(7*n-3)/2 for n in (0..50)] # _G. C. Greubel_, Aug 31 2019

%o (GAP) List([0..50], n-> n*(7*n-3)/2); # _G. C. Greubel_, Aug 31 2019

%Y Cf. A001106, A022264.

%Y Cf. numbers of the form n*(n*k-k+4)/2 listed in A226488 (this sequence is the case k=7). - _Bruno Berselli_, Jun 10 2013

%K nonn,easy

%O 0,2

%A _Philippe Deléham_, Mar 26 2013