A061165 Polynomial extrapolation of 2, 3, 5, 7, 11.

2, 3, 5, 7, 11, 22, 48, 100, 192, 341, 567, 893, 1345, 1952, 2746, 3762, 5038, 6615, 8537, 10851, 13607, 16858, 20660, 25072, 30156, 35977, 42603, 50105, 58557, 68036, 78622, 90398, 103450, 117867, 133741, 151167, 170243, 191070, 213752

Offset

1,1

Links

Harry J. Smith, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (5, -10, 10, -5, 1).

Formula

a(n) = (3n^4-34n^3+141n^2-206n+144)/24.

G.f.: x*(2-7*x+10*x^2-8*x^3+6*x^4)/(1-x)^5. [Colin Barker, Mar 28 2012]

a(1)=2, a(2)=3, a(3)=5, a(4)=7, a(5)=11, a(n)=5*a(n-1)-10*a(n-2)+ 10*a(n-3)- 5*a(n-4)+a(n-5). - Harvey P. Dale, Oct 05 2012

Example

a(6)=22 since first differences of (2,3,5,7,11) are (1,2,2,4), second differences (1,0,2), third differences (-1,2) and fourth differences (3), so a(6)=11+4+2+2+3=22.

Mathematica

Table[(3n^4-34n^3+141n^2-206n+144)/24, {n, 40}] (* or *) LinearRecurrence[ {5, -10, 10, -5, 1}, {2, 3, 5, 7, 11}, 40] (* Harvey P. Dale, Oct 05 2012 *)

Prog

(PARI) for (n=1, 1000, write("b061165.txt", n, " ", (3*n^4 - 34*n^3 + 141*n^2 - 206*n + 144)/24)) \\ Harry J. Smith, Jul 18 2009

Crossrefs

Cf. A061166.

Sequence in context: A038204 A075049 A361820 * A183055 A046689 A048278

Adjacent sequences: A061162 A061163 A061164 * A061166 A061167 A061168

Keyword

nonn,easy

Author

Henry Bottomley, Apr 18 2001

Status

approved