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!)
 A097947 G.f.: -(2+7*x+2*x^2)/(1+4*x-4*x^3-x^4). 2
 -2, 1, -6, 16, -62, 225, -842, 3136, -11706, 43681, -163022, 608400, -2270582, 8473921, -31625106, 118026496, -440480882, 1643897025, -6135107222, 22896531856, -85451020206, 318907548961, -1190179175642, 4441809153600, -16577057438762, 61866420601441, -230888624967006 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS One of 4 related sequences. This is the sequence "les(n)". "jes(n)" = [1, -4, 15, -56, ...] is (-1)^(n+1)*A001353(n+1), "tes(n)" is A097948 and "ves(n)" is A099949. LINKS Index entries for linear recurrences with constant coefficients, signature (-4,0,4,1). FORMULA Properties (from Creighton Dement, Sep 06 2004): I: jes(n) + les(n) + tes(n) = ves(n) II: All of the following are perfect squares: {les(2n+1); tes(2n+1); ves(2n+1); ves(2n+1) - jes(2n+1) - 1 = les(2n+1) + tes(2n+1) - 1; 3*les(2n+1) + 1 = 3*jes(n)^2 + 1}. III: les(2n+1) divides ves(2n+1) - jes(2n+1) - 1 = les(2n+1) + tes(2n+1) - 1 IV: (jes(n))^2 = les(2n+1) V: tes(2n) = A001570(n), sqrt( tes(2n+1) ) = A001075(n) VI: sqrt( ves(2n+1) ) = A001835(n) VII: sqrt( les(2n+1) ) = A001353(n) VIII: les(n) + tes(n) = ves(2+n) + jes(n) IX: lim n |jes(n+1)/jes(n)| = lim n |les(n+1)/les(n)| = lim n |tes(n+1)/tes(n)| = lim n |ves(n+1)/ves(n)| = 2 + sqrt(3) Comment from Roland Bacher, Sep 07 2004: These 4 sequences satisfy jes(n+1)=-4*jes(n)-jes(n-1), les(n+1)=les(n-1)+jes(n), ves(n+1)=les(n-1)-jes(n-1)+tes(n-1), tes(n+1)=les(n-1)+3*jes(n), plus initial conditions for n=0, 1. CROSSREFS Cf. A001353, A097948, A097949. Sequence in context: A254639 A049951 A025263 * A101032 A025271 A153804 Adjacent sequences:  A097944 A097945 A097946 * A097948 A097949 A097950 KEYWORD sign AUTHOR N. J. A. Sloane, following a suggestion of Creighton Dement, Sep 06 2004 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.