A211784 a(n) = n^2 + floor(n^2/2) + floor(n^2/3).
1, 7, 16, 29, 45, 66, 89, 117, 148, 183, 221, 264, 309, 359, 412, 469, 529, 594, 661, 733, 808, 887, 969, 1056, 1145, 1239, 1336, 1437, 1541, 1650, 1761, 1877, 1996, 2119, 2245, 2376, 2509, 2647, 2788, 2933, 3081, 3234, 3389, 3549, 3712, 3879
Offset: 1
Links
- Index entries for linear recurrences with constant coefficients, signature (1,1,0,-1,-1,1).
Programs
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Magma
[&+[Floor(n^2/k): k in [1..3]]: n in [1..46]]; // Bruno Berselli, May 06 2012
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Mathematica
f[n_, m_] := Sum[Floor[n^2/k], {k, 1, m}] t = Table[f[n, 3], {n, 1, 90}] FindLinearRecurrence[t] LinearRecurrence[{1, 1, 0, -1, -1, 1},{1, 7, 16, 29, 45, 66},46] (* Ray Chandler, Aug 02 2015 *)
Formula
a(n) = a(n-1)+a(n-2)-a(n-4)-a(n-5)+a(n-6) for n>=7.
G.f.: x*(1+6*x+8*x^2+6*x^3+x^4)/((1-x)^3*(1+2*x+2*x^2+x^3)). - Bruno Berselli, May 06 2012
a(n) = (66*n^2 + 9*(-1)^n - 17 - 4*A061347(n))/36. - Stefano Spezia, Nov 23 2023
Comments