|
%I #31 Sep 08 2022 08:46:06
%S 0,1,4,7,11,15,21,26,33,40,48,56,66,75,86,97,109,121,135,148,163,178,
%T 194,210,228,245,264,283,303,323,345,366,389,412,436,460,486,511,538,
%U 565,593,621,651,680,711,742,774,806,840,873,908,943,979
%N a(n) = n + floor(n/2 + n^2/3).
%C If a(k) is prime then k == 3, 4 or 8 (mod 12). The primes are 7, 11, 97, 109, 163, 283, 389, 593, 1129, 1987, 2039, 2713, ... .
%C This sequence is between A042965 and A236773.
%H Bruno Berselli, <a href="/A236771/b236771.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 (1,1,0,-1,-1,1).
%F G.f.: x*(1 + 3*x + 2*x^2 - 2*x^4) / ((1 + x)*(1 + x + x^2)*(1 - x)^3).
%F a(n) = a(n-1) + a(n-2) - a(n-4) - a(n-5) + a(n-6).
%F a(n) = (2*n*(2*n+9) - 2*(-1)^floor(2*(n-1)/3) + 3*(-1)^n - 5)/12.
%F a(n+2) - a(n) = A004772(n+4).
%F Also: a(n) = n + floor(n/2) + floor(n^2/3).
%t Table[n + Floor[n/2 + n^2/3], {n, 0, 60}]
%o (Magma) [n+Floor(n/2+n^2/3): n in [0..60]];
%Y Cf. A004772; A032766: n+floor(n/2).
%Y Cf. A042965: n+floor(1/2+n/3); A236773: n+floor(n^2/2+n^3/3).
%Y Cf. A281333: 1+floor(n/2)+floor(n^2/3).
%K nonn,easy
%O 0,3
%A _Bruno Berselli_, Feb 06 2014
|
