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

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A035028 First differences of A002002. 3
 4, 20, 104, 552, 2972, 16172, 88720, 489872, 2719028, 15157188, 84799992, 475894200, 2677788492, 15102309468, 85347160608, 483183316512, 2739851422820, 15558315261812, 88462135512712, 503569008273992, 2869602773253884, 16368396446913420, 93449566652932784 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 FORMULA a(n) = A049600(n, n-3). D-finite with recurrence: (n+2)*a(n) - (7*n+8)*a(n-1) + (7*n-8)*a(n-2) - (n-2)*a(n-3) = 0. - R. J. Mathar, Jan 28 2020 a(n) = ((n+1)*(n+3)*A001850(n+3) - (6*n^2 +22*n +17)*A001850(n+2) + (n+2)*(5*n+8)*A001850(n+1))/(2*(n+1)*(n+2)), A001850(n) = LegrndreP(n, 3). - G. C. Greubel, Oct 19 2022 MATHEMATICA Differences[CoefficientList[Series[((1-x)/Sqrt[1-6x+x^2]-1)/2, {x, 0, 30}], x]] (* Harvey P. Dale, Jun 04 2011 *) With[{P=LegendreP}, Table[(n*(n+2)*P[n+2, 3] -(6*n^2+10*n+1)*P[n+1, 3] +(n+1)*(5*n+ 3)*P[n, 3])/(2*n*(n+1)), {n, 30}]] (* G. C. Greubel, Oct 19 2022 *) PROG (Magma) I:=[4, 20, 104]; [n le 3 select I[n] else ( (7*n+1)*Self(n-1) - (7*n-15)*Self(n-2) + (n-3)*Self(n-3) )/(n+1): n in [1..30]]; // G. C. Greubel, Oct 19 2022 (SageMath) def A001850(n): return gen_legendre_P(n, 0, 3) def A035028(n): return ((n+1)*(n+3)*A001850(n+3) - (6*n^2 +22*n +17)*A001850(n+2) + (n+2)*(5*n+8)*A001850(n+1))/(2*(n+1)*(n+2)) [A035028(n) for n in range(40)] # G. C. Greubel, Oct 19 2022 CROSSREFS Cf. A001850, A002002, A035029, A049600. Sequence in context: A082761 A076035 A120978 * A104550 A089382 A291089 Adjacent sequences: A035025 A035026 A035027 * A035029 A035030 A035031 KEYWORD nonn AUTHOR EXTENSIONS More terms from Harvey P. Dale, Jun 04 2011 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 December 4 07:45 EST 2022. Contains 358544 sequences. (Running on oeis4.)