login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A114211 a(n) = (5*n^3+12*n^2+n+6)/6. 0
1, 4, 16, 42, 87, 156, 254, 386, 557, 772, 1036, 1354, 1731, 2172, 2682, 3266, 3929, 4676, 5512, 6442, 7471, 8604, 9846, 11202, 12677, 14276, 16004, 17866, 19867, 22012, 24306, 26754, 29361, 32132, 35072, 38186, 41479 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Column 3 of A114202. Third differences are 1,1,7,5,5,5,5,5,... with g.f. (1+6x^2-2x^3)/(1-x).

LINKS

Table of n, a(n) for n=0..36.

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

FORMULA

G.f.: (1+6*x^2-2*x^3)/(1-x)^4 = (1+3*(x/(1-x))+9*(x/(1-x))^2+5*(x/(1-x))^3)/(1-x).

a(n) = sum{k=0..n, C(n, k)*C(3, k)*J(k+1)} where J(n)=A001045(n).

a(0)=1, a(n)=a(n-1)+(n-1)*(n+2)+A104249(n).

EXAMPLE

[1,3,9,5]=[1*1,3*1,3*3,1*5]=[C(3,0)*J(1),C(3,1)*J(2),C(3,2)*J(3),C(3,3)*J(4)].

MATHEMATICA

CoefficientList[Series[(1+6x^2-2x^3)/(1-x)^4, {x, 0, 75}], x]  (* Harvey P. Dale, Mar 06 2011 *)

CROSSREFS

Sequence in context: A056373 A018828 A323847 * A188124 A190090 A227012

Adjacent sequences:  A114208 A114209 A114210 * A114212 A114213 A114214

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Nov 17 2005

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 August 20 03:33 EDT 2019. Contains 326139 sequences. (Running on oeis4.)