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A289870 a(n) = n*(n + 1) for n odd, otherwise a(n) = (n - 1)*(n + 1).

%I A289870 #21 Jul 14 2017 16:05:52
%S A289870 -1,2,3,12,15,30,35,56,63,90,99,132,143,182,195,240,255,306,323,380,
%T A289870 399,462,483,552,575,650,675,756,783,870,899,992,1023,1122,1155,1260,
%U A289870 1295,1406,1443,1560,1599,1722,1763,1892,1935,2070,2115,2256,2303,2450,2499
%N A289870 a(n) = n*(n + 1) for n odd, otherwise a(n) = (n - 1)*(n + 1).
%C A289870 a(n) is a fifth-order linear recurrence whose main interest is that it is related to (at least) eight other sequences (see the formula section).
%H A289870 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,2,-2,-1,1).
%F A289870 a(n) = (n + 1)*(n - 1 + (n mod 2)).
%F A289870 a(n) = n * A109613(n-1) for n>0.
%F A289870 a(n) = -A114285(n) * A109613(n).
%F A289870 a(n) = A002378(n) - A193356(n).
%F A289870 a(n) = A289296(-n).
%F A289870 a(n) = n^2 - (-1)^n * A093178(n).
%F A289870 a(2*k) = A000466(k).
%F A289870 G.f.: (1-3*x-3*x^2-3*x^3)/((-1+x)^3*(1+x)^2).
%t A289870 a[n_] := (n + 1)(n - 1 + Mod[n, 2]); Table[a[n], {n, 0, 50}]
%o A289870 (PARI) a(n)=if(n%2, n, n-1)*(n+1) \\ _Charles R Greathouse IV_, Jul 14 2017
%Y A289870 After -1, subsequence of A035106, A198442 and A214297.
%Y A289870 Cf. A000466, A002378, A093178, A109613, A114285, A124356, A193356, A289296.
%K A289870 sign,easy
%O A289870 0,2
%A A289870 _Jean-François Alcover_ and _Paul Curtz_, Jul 14 2017