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a(n) = A007678(2*n+1).
3

%I #17 Mar 08 2021 12:30:51

%S 0,1,11,50,154,375,781,1456,2500,4029,6175,9086,12926,17875,24129,

%T 31900,41416,52921,66675,82954,102050,124271,149941,179400,213004,

%U 251125,294151,342486,396550,456779,523625,597556,679056,768625,866779,974050,1090986,1218151,1356125

%N a(n) = A007678(2*n+1).

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).

%F From _Bruno Berselli_, Mar 08 2021: (Start)

%F G.f.: x*(1 + 6*x + 5*x^2 + 4*x^3)/(1 - x)^5.

%F a(n) = n*(2*n - 1)*(2*n^2 - n + 5)/6. (End)

%t Table[n (2 n - 1) (2 n^2 - n + 5)/6, {n, 0, 40}] (* _Bruno Berselli_, Mar 08 2021 *)

%o (Julia) [div(n*(2*n-1)*(2*n^2-n+5), 6) for n in 0:40] |> println # _Bruno Berselli_, Mar 08 2021

%Y Cf. A007678.

%Y See A341734 for the other bisection (rescaled).

%K nonn,easy

%O 0,3

%A _Scott R. Shannon_ and _N. J. A. Sloane_, Mar 07 2021

%E More terms from _Bruno Berselli_, Mar 08 2021