login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A061165 Polynomial extrapolation of 2, 3, 5, 7, 11. 2
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 (list; graph; refs; listen; history; text; internal format)
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: A297026 A038204 A075049 * A183055 A046689 A048278

Adjacent sequences:  A061162 A061163 A061164 * A061166 A061167 A061168

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 | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified February 28 05:46 EST 2020. Contains 332321 sequences. (Running on oeis4.)