This site is supported by donations to The OEIS Foundation.

 Annual appeal: Please make a donation to keep the OEIS running! Over 6000 articles have referenced us, often saying "we discovered this result with the help of the OEIS". Other ways to donate

 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 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 | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.