login
a(n) = (11*n^2 - 7*n)/2.
9

%I #62 Oct 14 2024 05:53:12

%S 0,2,15,39,74,120,177,245,324,414,515,627,750,884,1029,1185,1352,1530,

%T 1719,1919,2130,2352,2585,2829,3084,3350,3627,3915,4214,4524,4845,

%U 5177,5520,5874,6239,6615,7002,7400,7809,8229,8660

%N a(n) = (11*n^2 - 7*n)/2.

%C This sequence is related to A050441 by n*a(n) - Sum_{i=0..n-1} a(i) = 2*A050441(n). - _Bruno Berselli_, Aug 19 2010

%C Sum of n-th heptagonal number (A000566) and n-th octagonal number (A000567). - _Bruno Berselli_, Jun 11 2013

%C Create a triangle with T(r,1) = r^2 and T(r,c) = r^2 + r*c + c^2. The difference of the sum of the terms in row n and those in row n-1 is a(n). - _J. M. Bergot_, Jun 17 2013

%H B. Berselli, <a href="/A180223/b180223.txt">Table of n, a(n) for n = 0..10000</a>.

%H B. Berselli, A description of the recursive method in Comments lines: website <a href="http://www.lanostra-matematica.org/2008/12/sequenze-numeriche-e-procedimenti.html">Matem@ticamente</a> (in Italian).

%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+9*x)/(1-x)^3. - _Bruno Berselli_, Aug 19 2010 - corrected in Apr 18 2011

%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) with n>2. - _Bruno Berselli_, Aug 19 2010

%F a(n) = n + A226492(n). - _Bruno Berselli_, Jun 11 2013

%F E.g.f.: x*(4 + 11*x)*exp(x)/2. - _G. C. Greubel_, Aug 24 2015

%p A180223:=n->(11*n^2 - 7*n)/2; seq(A180223(n), n=0..30); # _Wesley Ivan Hurt_, Feb 25 2014

%t Table[(11*n^2 - 7*n)/2, {n, 0, 30}] (* _Wesley Ivan Hurt_, Feb 25 2014 *)

%t LinearRecurrence[{3,-3,1},{0,2,15},50] (* _Harvey P. Dale_, Oct 10 2020 *)

%o (PARI) a(n)=1/2*(11*n^2 - 7*n);

%o (Magma) [(11*n^2 - 7*n)/2: n in [0..30]]; // _Vincenzo Librandi_, Apr 18 2011

%o (Sage) [n*(11*n-7)/2 for n in (0..30)] # _G. C. Greubel_, Sep 18 2019

%o (GAP) List([0..30], n-> n*(11*n-7)/2); # _G. C. Greubel_, Sep 18 2019

%Y Cf. A050441, A000566, A000567, A226492.

%Y Cf. numbers of the form n*(n*k-k+4)/2 listed in A226488 (this sequence is the case k=11). - _Bruno Berselli_, Jun 10 2013

%K nonn,easy

%O 0,2

%A Graziano Aglietti (mg5055(AT)mclink.it), Aug 16 2010