A130656 Interlacing n^3/2 and n^2(n + 1)/2.
1, 4, 18, 32, 75, 108, 196, 256, 405, 500, 726, 864, 1183, 1372, 1800, 2048, 2601, 2916, 3610, 4000, 4851, 5324, 6348, 6912, 8125, 8788, 10206, 10976, 12615, 13500, 15376, 16384, 18513, 19652, 22050, 23328, 26011, 27436, 30420, 32000, 35301, 37044
Offset: 1
Links
- Index entries for linear recurrences with constant coefficients, signature (1,3,-3,-3,3,1,-1).
Programs
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Maple
A130656:=n->n^2 * floor((n + 1)/2): seq(A130656(n), n=1..100); # Wesley Ivan Hurt, Jan 21 2017
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Mathematica
a[n_Integer] := n^2 * Floor[(n + 1)/2] LinearRecurrence[{1,3,-3,-3,3,1,-1},{1,4,18,32,75,108,196},50] (* Harvey P. Dale, Feb 18 2015 *)
Formula
a(n) = n^2 * floor((n + 1)/2).
G.f.: x*(1+3*x+11*x^2+5*x^3+4*x^4)/((1-x)^4*(1+x)^3). - R. J. Mathar, Sep 09 2008
a(n) = a(n-1)+ 3*a(n-2)-3*a(n-3)-3*a(n-4)+3*a(n-5)+a(n-6)-a(n-7), a(1)=1, a(2)=4, a(3)=18, a(4)=32, a(5)=75, a(6)=108, a(7)=196. - Harvey P. Dale, Feb 18 2015
Sum_{n>=1} 1/a(n) = zeta(3)/4 + Pi^2/4 - 2*log(2). - Amiram Eldar, Mar 15 2024