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%I #16 Oct 13 2020 23:29:32
%S 0,1,3,7,14,24,38,57,81,111,148,192,244,305,375,455,546,648,762,889,
%T 1029,1183,1352,1536,1736,1953,2187,2439,2710,3000,3310,3641,3993,
%U 4367,4764,5184,5628,6097,6591,7111,7658,8232,8834,9465,10125,10815,11536
%N Nearest integer to (n+1)^3/9.
%H Harry J. Smith, <a href="/A060999/b060999.txt">Table of n, a(n) for n=0..1000</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,2,-3,3,-1).
%F G.f.: x*(1+x^2)/((1-x)^3*(1-x^3)).
%F Expansion of x * (1 - x^4) / ((1 - x)^3 * (1 - x^2) * (1 - x^3)) in powers of x.
%F Euler transform of length 4 sequence [ 3, 1, 1, -1]. - _Michael Somos_, Aug 12 2009
%F a(-2-n) = -a(n). - _Michael Somos_, Aug 12 2009
%F G.f.: ( (1 + 4*x + x^2) / (1 - x)^4 - 1 / (1 + x + x^2) ) / 9.
%e x + 3*x^2 + 7*x^3 + 14*x^4 + 24*x^5 + 38*x^6 + 57*x^7 + 81*x^8 + ...
%t Table[Floor[(n+1)^3/9+1/2],{n,0,50}] (* _Harvey P. Dale_, Jan 20 2013 *) (* or *)
%t LinearRecurrence[{3, -3, 2, -3, 3, -1}, {0, 1, 3, 7, 14, 24}, 47] (* _Georg Fischer_, Oct 13 2020 *)
%o (PARI) { default(realprecision, 100); for (n=0, 1000, write("b060999.txt", n, " ", round((n + 1)^3/9)) ) } \\ _Harry J. Smith_, Jul 16 2009
%o (PARI) {a(n) = n++; (n^3 - kronecker(-3, n)) / 9} /* _Michael Somos_, Aug 12 2009 */
%K nonn
%O 0,3
%A _N. J. A. Sloane_, May 14 2001
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