The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A061166 Polynomial extrapolation of 2, 3, 5, 7, 11, 13, 17. 1
 2, 3, 5, 7, 11, 13, 17, 72, 332, 1139, 3129, 7361, 15469, 29837, 53797, 91850, 149910, 235571, 358397, 530235, 765551, 1081789, 1499753, 2044012, 2743328, 3631107, 4745873, 6131765, 7839057, 9924701, 12452893, 15495662, 19133482, 23455907 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Table of n, a(n) for n=1..34. Index entries for linear recurrences with constant coefficients, signature (7, -21, 35, -35, 21, -7, 1). FORMULA a(n) = (23n^6-537n^5+4925n^4-22515n^3+53732n^2-61548n+27360)/720. G.f.: x*(2-11*x+26*x^2-35*x^3+32*x^4-29*x^5+38*x^6)/(1-x)^7. [Colin Barker, Mar 28 2012] EXAMPLE a(8)=72 since first differences of (2,3,5,7,11,13,17) are (1,2,2,4,2,4), second differences (1,0,2,-2,2), third differences (-1,2,-4,4), fourth differences (3,-6,8), fifth differences (-9,14) and sixth differences (23) so a(8)=17+4+2+4+8+14+23=72. MATHEMATICA CoefficientList[Series[x (2-11x+26x^2-35x^3+32x^4-29x^5+38x^6)/(1-x)^7, {x, 0, 50}], x] (* or *) LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {2, 3, 5, 7, 11, 13, 17}, 50] (* Harvey P. Dale, Aug 14 2021 *) CROSSREFS Cf. A061165. Sequence in context: A265408 A053434 A241716 * A003681 A217147 A029732 Adjacent sequences: A061163 A061164 A061165 * A061167 A061168 A061169 KEYWORD nonn,easy AUTHOR Henry Bottomley, Apr 18 2001 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 May 20 10:42 EDT 2024. Contains 372712 sequences. (Running on oeis4.)