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!)
A277228 Convolution of the even-indexed triangular numbers (A014105) and the squares (A000290). 2
0, 0, 3, 22, 88, 258, 623, 1316, 2520, 4476, 7491, 11946, 18304, 27118, 39039, 54824, 75344, 101592, 134691, 175902, 226632, 288442, 363055, 452364, 558440, 683540, 830115, 1000818, 1198512, 1426278, 1687423, 1985488, 2324256, 2707760, 3140291, 3626406 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

This sequence was originally proposed in a comment on A071245 by J. M. Bergot as giving the first differences. Therefore, a(n) gives the partial sums of A071245.

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

FORMULA

O.g.f.: x^2*(1 + x)*(3 + x)/(1 - x)^6 = (x*(3 + x)/(1 - x)^3)*(x*(1 + x)/(1 - x)^3).

a(n) = Sum_{k=0..n} A014105(n-k)*A000290(k).

a(n) = binomial(n+1, 3)*(4*n^2 + 5*n + 4)/10 = (n - 1)*n*(n + 1)*(4*n^2 + 5*n + 4)/60.

a(n) = Sum_{k=0..n} A071245(k).

a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>5. - Colin Barker, Oct 21 2016

MATHEMATICA

Table[(n - 1) n (n + 1) (4 n^2 + 5 n + 4)/60, {n, 0, 40}] (* Bruno Berselli, Oct 21 2016 *)

PROG

(PARI) concat(vector(2), Vec(x^2*(1+x)*(3+x)/(1-x)^6 + O(x^50))) \\ Colin Barker, Oct 21 2016

(MAGMA) [Binomial(n+1, 3)*(4*n^2 +5*n +4)/10: n in [0..40]]; // G. C. Greubel, Oct 22 2018

CROSSREFS

Cf. A000217, A000290, A014105, A071245.

Sequence in context: A135836 A004305 A275290 * A302272 A302723 A095663

Adjacent sequences:  A277225 A277226 A277227 * A277229 A277230 A277231

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, Oct 20 2016

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 April 3 13:53 EDT 2020. Contains 333197 sequences. (Running on oeis4.)