login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A299120 a(n) = (n-1)*(n-2)*(n+3)*(n+2)/12. 2
1, 0, 0, 5, 21, 56, 120, 225, 385, 616, 936, 1365, 1925, 2640, 3536, 4641, 5985, 7600, 9520, 11781, 14421, 17480, 21000, 25025, 29601, 34776, 40600, 47125, 54405, 62496, 71456, 81345, 92225, 104160, 117216, 131461, 146965, 163800, 182040, 201761, 223041 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Colin Barker, Table of n, a(n) for n = 0..1000

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

FORMULA

a(n) = n^4/12 + n^3/6 - 7n^2/12 - 2n/3 + 1 = (n-1)*(n-2)*(n+3)*(n+2)/12. .

From Colin Barker, Feb 05 2018: (Start)

G.f.: (1 - 5*x + 10*x^2 - 5*x^3 + x^4) / (1 - x)^5.

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5. (End)

a(n) = A033275(n+2) for n > 1. - Georg Fischer, Oct 09 2018

From Amiram Eldar, Jan 12 2021: (Start)

Sum_{n>=3} 1/a(n) = 43/150.

Sum_{n>=3} (-1)^(n+1)/a(n) = 16*log(2)/5 - 154/75. (End)

MAPLE

seq(n^4/12+n^3/6-7*n^2/12-2*n/3+1, n=0..10^3); # Muniru A Asiru, Feb 04 2018

MATHEMATICA

Rest@ CoefficientList[Series[(1 - 5 x + 10 x^2 - 5 x^3 + x^4)/(1 - x)^5, {x, 0, 41}], x] (* Michael De Vlieger, Feb 10 2018 *)

f[n_] := n^4/12 + n^3/6 - 7*n^2/12 - 2*n/3 + 1; Array[f, 40, 0] (* or *)

LinearRecurrence[{5, -10, 10, -5, 1}, {1, 0, 0, 5, 21}, 40] (* Robert G. Wilson v, Mar 12 2018 *)

PROG

(Magma) [n^4/12 + n^3/6 - 7*n^2/12 - 2*n/3 + 1: n in [0..40]];

(GAP) List([0..10^3], n->n^4/12+n^3/6-7*n^2/12-2*n/3+1); # Muniru A Asiru, Feb 04 2018

(PARI) Vec((1 - 5*x + 10*x^2 - 5*x^3 + x^4) / (1 - x)^5 + O(x^50)) \\ Colin Barker, Feb 05 2018

CROSSREFS

Cf. A001263, A033275, A077415, A299146, A299198.

Sequence in context: A096942 A122244 A146854 * A033275 A166464 A059859

Adjacent sequences: A299117 A299118 A299119 * A299121 A299122 A299123

KEYWORD

nonn,easy

AUTHOR

Juri-Stepan Gerasimov, Feb 03 2018

EXTENSIONS

Edited by Wolfdieter Lang, Apr 06 2018

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 30 19:14 EST 2022. Contains 358453 sequences. (Running on oeis4.)