%I #27 Sep 08 2022 08:45:01
%S 11,42,93,164,255,366,497,648,819,1010,1221,1452,1703,1974,2265,2576,
%T 2907,3258,3629,4020,4431,4862,5313,5784,6275,6786,7317,7868,8439,
%U 9030,9641,10272,10923,11594,12285,12996,13727,14478,15249,16040,16851,17682,18533
%N a(n) = 10*n^2+n.
%C a(n) = A055436(n) if 1<=n<10.
%C Number of edges in the join of the complete 4-partite graph of order 4n and the cycle graph of order n, K_n,n,n,n * C_n. - _Roberto E. Martinez II_, Jan 07 2002
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F From _Bruno Berselli_, Nov 26 2013: (Start)
%F G.f.: x*(11 + 9*x) / (1 - x)^3.
%F a(n) = Sum_{i=0..2*n} (-1)^i*(2*n+i)^2.
%F a(n) = Sum_{i=1..2*n} (-1)^i*(4*n+i)^2. (End)
%F From _Wesley Ivan Hurt_, Apr 27 2016: (Start)
%F a(n) = 3*a(n-1)-3*a(n-2)+a(n-3) for n>3.
%F a(n) = (1/5) * Sum_{i=0..10*n} i. (End)
%F E.g.f.: x*(11 + 10*x)*exp(x). - _Ilya Gutkovskiy_, Apr 27 2016
%F a(n) = A000217(6*n) - A000217(4*n). - _Bruno Berselli_, Sep 21 2016
%e From the third formula: a(8) = 648 = 16^2 -17^2 +18^2 ... +30^2 -31^2 +32^2 = -33^2 +34^2 -35^2 ... +46^2 -47^2 +48^2.
%p A055437:=n->10*n^2+n: seq(A055437(n), n=1..50); # _Wesley Ivan Hurt_, Apr 27 2016
%t Table[10 n^2 + n, {n, 50}] (* _Wesley Ivan Hurt_, Apr 27 2016 *)
%o (Magma) [10*n^2+n : n in [1..50]]; // _Wesley Ivan Hurt_, Apr 27 2016
%o (PARI) a(n)=10*n^2+n \\ _Charles R Greathouse IV_, Jun 17 2017
%Y Cf. A000217, A002378, A055436, A055438.
%K nonn,easy
%O 1,1
%A _Henry Bottomley_, May 18 2000