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A023001 interleaved with 2*A023001 and 4*A023001.
2

%I #35 Jul 25 2024 03:44:45

%S 0,0,0,1,2,4,9,18,36,73,146,292,585,1170,2340,4681,9362,18724,37449,

%T 74898,149796,299593,599186,1198372,2396745,4793490,9586980,19173961,

%U 38347922,76695844,153391689,306783378,613566756,1227133513,2454267026,4908534052

%N A023001 interleaved with 2*A023001 and 4*A023001.

%C A033138 with three zeros prepended. - _Joerg Arndt_, Mar 10 2015

%H Vincenzo Librandi, <a href="/A155803/b155803.txt">Table of n, a(n) for n = 0..1000</a>

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

%F a(3n) = A023001(n). a(3n+1) = 2*A023001(n) = A125835(n). a(3n+2) = 4*A023001(n).

%F a(n) = a(n-3)+2^(n-3) = a(n-3)+A000079(n-3). Here, a(.) can also be one of its higher order differences.

%F a(n) = 2*a(n-1)+a(n-3)-2*a(n-4). G.f.: x^3/((x-1)*(2*x-1)*(1+x+x^2)). [_R. J. Mathar_, Jul 23 2009]

%F a(n) = floor(2^n/7). [_Mircea Merca_, Dec 22 2010]

%p A023001 := proc(n) (8^n-1)/7; end: A155803 := proc(n) RETURN( A023001(n),2*A023001(n),4*A023001(n)) ; end: L := [seq(A155803(n),n=0..30)] ; # _R. J. Mathar_, Jul 23 2009

%p seq(floor(2^n/7),n=0..30) # _Mircea Merca_, Dec 22 2010

%t CoefficientList[Series[x^3/(1-2 x-x^3+2 x^4), {x,0,50}],x] (* _Harvey P. Dale_, Mar 13 2011 *)

%o (Magma) [Floor(2^n/7): n in [0..40]]; // _Vincenzo Librandi_, Sep 17 2011

%K nonn,easy

%O 0,5

%A _Paul Curtz_, Jan 27 2009

%E Edited and extended by _R. J. Mathar_, Jul 23 2009