This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A179894 Given the series (1, 2, 1, 2, 1, 2,...), let (1 + 2x + x^2 + 2x^3 + ...) * (1 + 2x^2 + x^3 + 2x^4 + ...) = (1 + 2x + 3x^2 + 7x^3 + ...) 1
 1, 2, 3, 7, 7, 12, 11, 17, 15, 22, 19, 27, 23, 32, 27, 37, 31, 42, 35, 47, 39, 52, 43, 57, 47, 62, 51, 67, 55, 72, 59, 77, 63, 82, 67, 87, 71, 92, 75, 97, 79, 102, 83, 107, 87, 112, 91, 117, 95, 122, 99, 127, 103, 132, 107, 137, 111, 142, 115, 147, 119, 152, 123, 157, 127, 162 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The offset has been selected as "1" to accommodate the conjectured property of the sequence: 3 divides a(n) iff n == 0 mod 3. Example: 3 divides (3, 12, 15, 27, 27, 42,...) but not other terms through n = 18. LINKS Index entries for linear recurrences with constant coefficients, signature (0,2,0,-1). FORMULA (1 + 2x + 3x^2 + 7x^3 + ...) = (1 + 2x + x^2 + 2x^3 + ...) * (1 + 2x^2 + x^3 + 2x^4 + ...). Let M = a triangle with (1, 2, 1, 2, 1, 2,..) in every column with the leftmost column shifted upwards one row. Then A179894 = leftmost column of M^2. a(1)=1; for odd n>1, a(n)=2*n-3; for even n, a(n)=5*n/2-3. So it is true that 3 divides a(n) iff 3 divides n. - Jon E. Schoenfield, Jul 31 2010 a(n) = ((9+(-1)^n)*n-12)/4 for n>1. a(n) = 2*a(n-2)-a(n-4) for n>5. G.f.: x*(2*x+1)*(x^3+x^2+1)/((x-1)^2*(x+1)^2). - Colin Barker, Oct 28 2012 MAPLE t1:=add(x^(2*n), n=0..50)+2*add(x^(2*n+1), n=0..50); t2:=2*add(x^(2*n), n=0..50)-1+add(x^(2*n+1), n=0..50)-x; t3:=t1*t2; series(t3, x, 100); seriestolist(%); CROSSREFS Sequence in context: A305420 A171464 A276730 * A085420 A027672 A322138 Adjacent sequences:  A179891 A179892 A179893 * A179895 A179896 A179897 KEYWORD nonn,easy AUTHOR Gary W. Adamson, Jul 31 2010 EXTENSIONS Edited, corrected and extended by N. J. A. Sloane and Jon E. Schoenfield, Sep 06 2010 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
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified March 18 22:11 EDT 2019. Contains 321305 sequences. (Running on oeis4.)