A178978 - OEIS

%I #17 Mar 07 2022 02:06:03

%S 0,2,5,1,14,20,1,35,44,2,65,77,10,104,119,5,152,170,7,209,230,28,275,

%T 299,4,350,377,5,434,464,55,527,560,22,629,665,26,740,779,91,860,902,

%U 35,989,1034,40,1127,1175,136,1274,1325,17

%N a(n) = A144448(n+1)/8.

%C Differs from A178971 for indices n > 23.

%H G. C. Greubel, <a href="/A178978/b178978.txt">Table of n, a(n) for n = 0..5000</a>

%H <a href="/index/Rec#order_81">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1).

%F Trisections:

%F   a(3*n)   = A145911(n);

%F   a(3*n+1) = A145910(n);

%F   a(3*n+2) = A178977(n).

%F a(n) = 3*a(n-27) - 3*a(n-54) + a(n-81). - _G. C. Greubel_, Mar 06 2022

%p A061039 := proc(n) numer(1/9-1/n^2) ; end proc:

%p A144448 := proc(n) A061039(1+2*n) ; end proc:

%p A178978 := proc(n) A144448(n+1)/8 ; end proc:

%p seq(A178978(n),n=0..80) ; # _R. J. Mathar_, Jan 06 2011

%t Table[Numerator[1/9 -1/(2*n+3)^2]/8, {n, 0, 75}] (* _G. C. Greubel_, Mar 06 2022 *)

%o (Sage) [numerator(1/9 -1/(2*n+3)^2)/8 for n in (0..75)] # _G. C. Greubel_, Mar 06 2022

%Y Cf. A061039, A145910, A145911, A178971, A178977, A178978, A144448.

%K nonn,easy,less

%O 0,2

%A _Paul Curtz_, Jan 02 2011