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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
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
KEYWORD
nonn,easy
AUTHOR
Henry Bottomley, Apr 18 2001
STATUS
approved

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Last modified May 20 10:42 EDT 2024. Contains 372712 sequences. (Running on oeis4.)