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A286264 a(n) = 2*(ceiling((n^2)/2)+1) - 1. 2

%I #42 Sep 08 2022 08:46:19

%S 3,5,11,17,27,37,51,65,83,101,123,145,171,197,227,257,291,325,363,401,

%T 443,485,531,577,627,677,731,785,843,901,963,1025,1091,1157,1227,1297,

%U 1371,1445,1523,1601,1683,1765,1851,1937,2027,2117,2211,2305,2403,2501

%N a(n) = 2*(ceiling((n^2)/2)+1) - 1.

%H Colin Barker, <a href="/A286264/b286264.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,-2,1).

%F a(n) > n^2.

%F From _Colin Barker_, May 05 2017: (Start)

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

%F a(n) = 3/2 - (-1)^n/2 + n^2.

%F a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4) for n>4.

%F (End)

%e n=2: (1*3*5*7)/(2*4*6*8)=(1*1*5*7)/(2*4*2*8) => a(2)=5=A151800(2^2);

%e n=3: (1*3*5*7*9*11*13*15*17)/(2*4*6*8*10*12*14*16*18)=(1*1*1*1*1*11*13*15*17)/(2*4*2*8*2*12*2*16*2) => a(3)=11=A151800(3^2).

%p A286264:=n->3/2 - (-1)^n/2 + n^2: seq(A286264(n), n=1..100); # _Wesley Ivan Hurt_, May 05 2017

%t Table[2 (Ceiling[n^2/2] + 1) - 1, {n, 1, 40}]

%o (PARI) Vec(x*(3 - x + x^2 + x^3) / ((1 - x)^3*(1 + x)) + O(x^60)) \\ _Colin Barker_, May 05 2017

%o (Magma) [3/2 - (-1)^n/2 + n^2 : n in [1..100]]; // _Wesley Ivan Hurt_, May 05 2017

%Y Cf. A007918 (nextprime), A151800 (version 2).

%K nonn,easy

%O 1,1

%A _Ralf Steiner_, May 05 2017

%E More terms from _Colin Barker_, May 05 2017

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Last modified March 28 10:55 EDT 2024. Contains 371241 sequences. (Running on oeis4.)