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!)
 A140870 8*P_4(2n), 8 times the Legendre Polynomial of order 4 at 2n. 2
 3, 443, 8483, 44283, 141443, 347003, 721443, 1338683, 2286083, 3664443, 5588003, 8184443, 11594883, 15973883, 21489443, 28323003, 36669443, 46737083, 58747683, 72936443, 89552003, 108856443, 131125283, 156647483, 185725443, 218675003, 255825443 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 LINKS Eric W. Weisstein, Legendre Polynomial. Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1). FORMULA Legendre polynomial LP_4(x) = (35*x^4-30*x^2+3)/8. - Klaus Brockhaus, Nov 21 2009 From Klaus Brockhaus, Nov 21 2009: (Start) a(n) = 560*n^4-120*n^2+3. a(n) = 4*a(n-1)-6*a(n-2)+4*a(n-3)-a(n-4)+13440 for n > 3; a(0)=3, a(1)=443, a(2)=8483, a(3)=44283. G.f.: (3+428*x+6298*x^2+6268*x^3+443*x^4)/(1-x)^5. (End) MAPLE A140870 := proc(n)         8*orthopoly[P](4, 2*n) ; end proc: # R. J. Mathar, Oct 24 2011 MATHEMATICA Table[8 LegendreP[4, 2n], {n, 0, 50}] LinearRecurrence[{5, -10, 10, -5, 1}, {3, 443, 8483, 44283, 141443}, 30] (* Vincenzo Librandi, Oct 04 2015 *) PROG (MAGMA) P := PolynomialRing(IntegerRing()); LP4:=LegendrePolynomial(4); [ Evaluate(8*LP4, 2*n): n in [0..26] ]; // Klaus Brockhaus, Nov 18 2009 (PARI) {for(n=0, 26, print1(subst(8*pollegendre(4), x, 2*n), ", "))} \\ Klaus Brockhaus, Nov 21 2009 (MAGMA) [560*n^4 - 120*n^2 + 3: n in [0..30]]; // Vincenzo Librandi, Oct 04 2015 CROSSREFS Cf. A144124. Sequence in context: A086207 A092052 A139999 * A157601 A094454 A261004 Adjacent sequences:  A140867 A140868 A140869 * A140871 A140872 A140873 KEYWORD nonn,easy AUTHOR N. J. A. Sloane, Nov 17 2009 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.