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A082742 Indices of occurrences of 2 in A004738. 0

%I

%S 2,4,6,8,12,14,20,22,30,32,42,44,56,58,72,74,90,92,110,112,132,134,

%T 156,158,182,184,210,212,240,242,272,274,306,308,342,344,380,382,420,

%U 422,462,464,506,508,552,554,600,602,650,652,702,704,756,758,812,814,870,872,930,932,992,994,1056,1058,1122,1124,1190,1192,1260,1262,1332,1334,1406,1408,1482,1484,1560,1562

%N Indices of occurrences of 2 in A004738.

%C Indices of occurrences of 1 in A004738 are given by A002061, b(n) = n^2 - n + 1 (the central polygonal numbers). All entries are even.

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,2,-2,-1,1).

%F G.f.: 2*x*(1+x-x^2-x^3+x^4)/((1+x)^2*(1-x)^3). - _Charles R Greathouse IV_, Feb 03 2013

%F a(n) = 2*A134519(n). - _R. J. Mathar_, Feb 03 2013

%p A004738 := proc(n)

%p local f ;

%p f := floor(sqrt(n)+1/2) ;

%p f+1-abs(n-1-f^2) ;

%p end proc:

%p for n from 1 to 1600 do

%p if A004738(n) = 2 then

%p printf("%d,",n) ;

%p end if;

%p end do: # _R. J. Mathar_, Feb 03 2013

%t LinearRecurrence[{1,2,-2,-1,1},{2,4,6,8,12},80] (* _Harvey P. Dale_, Jun 16 2017 *)

%o (PARI) a(n)=(n^2+2*n+8+if(n%2,2*n-5))/4 \\ _Charles R Greathouse IV_, Feb 03 2013

%Y Cf. A004738.

%K nonn,easy

%O 1,1

%A _Amarnath Murthy_, Apr 15 2003

%E More terms from _R. J. Mathar_, Feb 03 2013

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Last modified February 24 13:05 EST 2020. Contains 332209 sequences. (Running on oeis4.)