A061166 Polynomial extrapolation of 2, 3, 5, 7, 11, 13, 17.

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

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