A086689 a(n) = Sum_{i=1..n} i^2*t(i), where t = A000217.

1, 13, 67, 227, 602, 1358, 2730, 5034, 8679, 14179, 22165, 33397, 48776, 69356, 96356, 131172, 175389, 230793, 299383, 383383, 485254, 607706, 753710, 926510, 1129635, 1366911, 1642473, 1960777, 2326612, 2745112

Offset

1,2

Comments

This sequence is related to A001296 by a(n) = n*A001296(n) - Sum_{i=0..n-1} A001296(i) with n>0. - Bruno Berselli, Jan 21 2013

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

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

Formula

a(n) = n*(n+1)*(n+2)*(12*n^2+9*n-1)/120.

G.f.: x*(1+7*x+4*x^2) / (x-1)^6. - R. J. Mathar, Sep 15 2012

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). - Wesley Ivan Hurt, Nov 19 2014

a(n) = Sum_{i=1..n} ( i*Sum_{k=1..i} i*k ). - Wesley Ivan Hurt, Nov 19 2014

Example

a(4) = 227 = 1^2*A000217(1)+2^2*A000217(2)+3^2*A000217(3)+4^2*A000217(4).

Maple

A086689:=n->n*(n+1)*(n+2)*(12*n^2+9*n-1)/120: seq(A086689(n), n=1..40); # Wesley Ivan Hurt, Nov 19 2014

Mathematica

Table[n (n + 1) (n + 2) (12 n^2 + 9 n - 1)/120, {n, 40}] (* Wesley Ivan Hurt, Nov 19 2014 *)
CoefficientList[Series[(1 + 7 x + 4 x^2) / (x - 1)^6, {x, 0, 50}], x] (° Vincenzo Librandi, Nov 20 2014 °)

Prog

(PARI) t(n)=n*(n+1)/2 for(i=1, 30, print1(", "sum(j=1, i, j^2*t(i))))
(Magma) [n*(n+1)*(n+2)*(12*n^2+9*n-1)/120 : n in [1..40]]; // Wesley Ivan Hurt, Nov 19 2014

Crossrefs

Cf. A001296.

Sequence in context: A067863 A257809 A106975 * A141956 A290244 A137720

Adjacent sequences: A086686 A086687 A086688 * A086690 A086691 A086692

Keyword

nonn,easy

Author

Jon Perry, Jul 28 2003

Status

approved