A155803 A023001 interleaved with 2*A023001 and 4*A023001.

0, 0, 0, 1, 2, 4, 9, 18, 36, 73, 146, 292, 585, 1170, 2340, 4681, 9362, 18724, 37449, 74898, 149796, 299593, 599186, 1198372, 2396745, 4793490, 9586980, 19173961, 38347922, 76695844, 153391689, 306783378, 613566756, 1227133513, 2454267026, 4908534052

Offset: 0

Author

Paul Curtz, Jan 27 2009

Keywords

• nonn
• easy

Comments

A033138 with three zeros prepended. - Joerg Arndt, Mar 10 2015

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (2,0,1,-2).

Programs

Magma

[Floor(2^n/7): n in [0..40]]; // Vincenzo Librandi, Sep 17 2011

Maple

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
seq(floor(2^n/7),n=0..30) # Mircea Merca, Dec 22 2010

Mathematica

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

Formula

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

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.

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]

a(n) = floor(2^n/7). [Mircea Merca, Dec 22 2010]

Extensions

Edited and extended by R. J. Mathar, Jul 23 2009