A259713 - OEIS

%I #26 Nov 14 2024 23:22:19

%S 1,8,10,26,46,98,190,386,766,1538,3070,6146,12286,24578,49150,98306,

%T 196606,393218,786430,1572866,3145726,6291458,12582910,25165826,

%U 50331646,100663298,201326590,402653186,805306366,1610612738,3221225470,6442450946,12884901886

%N a(n) = 3*2^n - 2*(-1)^n.

%C Inverse binomial transform of 3^n, with 3 (second term) excluded.

%C a(n) mod 9 gives A010689.

%H Colin Barker, <a href="/A259713/b259713.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (1,2).

%F a(n) = a(n-1) + 2*a(n-2) for n>1, a(0)=1, a(1)=8.

%F a(n) = 2*a(n-1) - 6*(-1)^n for n>0, a(0)=1.

%F a(4n+2) = 10*A182460(n); a(2n) = A096045(n), a(2n+1) = A140788(n).

%F a(n) = 3*A014551(n+1) - A201630(n).

%F a(n+2) - a(n) = a(n) + a(n+1) = A005010(n).

%F G.f.: -(7*x+1) / ((x+1)*(2*x-1)). - _Colin Barker_, Jul 03 2015

%t Table[3 2^n - 2 (-1)^n, {n, 0, 50}] (* _Vincenzo Librandi_, Jul 04 2015 *)

%t LinearRecurrence[{1,2},{1,8},40] (* _Harvey P. Dale_, Aug 19 2020 *)

%o (PARI) Vec(-(7*x+1)/((x+1)*(2*x-1)) + O(x^100)) \\ _Colin Barker_, Jul 03 2015

%o (Magma) [3*2^n-2*(-1)^n: n in [0..40]]; // _Vincenzo Librandi_, Jul 04 2015

%Y Cf. A000244, A005010, A007283, A010689, A096045, A140788, A182460, A201630.

%K nonn,easy

%O 0,2

%A _Paul Curtz_, Jul 03 2015

%E Typo in data fixed by _Colin Barker_, Jul 03 2015