The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A094627 Expansion of (1+x)^2/((1-x)*(1-10*x^2)). 1
 1, 3, 14, 34, 144, 344, 1444, 3444, 14444, 34444, 144444, 344444, 1444444, 3444444, 14444444, 34444444, 144444444, 344444444, 1444444444, 3444444444, 14444444444, 34444444444, 144444444444, 344444444444, 1444444444444 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS The digital sum of the n-th term is 2n+1. a(n) = floor(10^floor(n/2)*(2-(-1)^n+4/9)) = 1,3,14,34,144,344,... (i.e. 2-(-1)^n = 1 for even n, 3 for odd n, followed by floor(n/2) digits '4'.) - M. F. Hasler LINKS Table of n, a(n) for n=0..24. Index entries for linear recurrences with constant coefficients, signature (1,10,-10). FORMULA a(n) = 10^(n/2)*( 31*sqrt(10)/180 +13/18 -(31*sqrt(10)/180-13/18)*(-1)^n )-4/9. a(n) = (13*b(n)+31*b(n-1)-4)/9 with b(n) = 1,0,10,0,100,0,1000,.. (aerated A011557) [R. J. Mathar, Nov 26 2010] EXAMPLE (x^2 + 2*x + 1)/(10*x^3 - 10*x^2 - x + 1) = 1 + 3*x + 14*x^2 + 34*x^3 + 144*x^4 + 344*x^5 + 1444*x^6 + 3444*x^7 + 14444*x^8 + ... MAPLE A011557aer := proc(n) if type(n, 'odd') then 0 ; else 10^(n/2) ; end if; end proc: A094627 := proc(n) (13*A011557aer(n)+31*A011557aer(n-1)-4)/9 ; end proc: seq(A094627(n), n=0..10) ; # R. J. Mathar, Nov 16 2010 MATHEMATICA sr[n_, nn_]:=Table[FromDigits[PadRight[{n}, i, 4]], {i, nn}]; With[{nn=20}, Sort[ Join[ sr[ 1, nn], sr[3, nn]]]] (* Harvey P. Dale, May 25 2014 *) CROSSREFS Cf. A094626. Sequence in context: A140064 A064226 A077288 * A009394 A076533 A081379 Adjacent sequences: A094624 A094625 A094626 * A094628 A094629 A094630 KEYWORD easy,nonn AUTHOR Paul Barry, May 15 2004 EXTENSIONS Swapped the generic comment and the specific definition; added Maple prog. STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 31 11:52 EDT 2023. Contains 363066 sequences. (Running on oeis4.)