A213788 a(n) = Sum_{1<=i<j<k<=n} P(i)*P(j)*P(k), where P(m) is the k-th Pell number A000129(m).

0, 0, 0, 10, 214, 3491, 52001, 748788, 10636260, 150248190, 2117562834, 29816257390, 419662506490, 5905775317025, 83104503504515, 1169392060102440, 16454728773220584, 231536384221100316, 3257968708458764196, 45843125116860034258, 645061876629223784830, 9076710308820189950975

Offset

0,4

Links

Alois P. Heinz, Table of n, a(n) for n = 0..275

Index entries for linear recurrences with constant coefficients, signature (21,-98,-34,616,-532,-62,98,-7,-1).

Formula

G.f.: (x^4+2*x^3-23*x^2+4*x+10)*x^3 / ((x-1) * (x^2+14*x-1) * (x^2-2*x-1) * (x^2+2*x-1) * (x^2-6*x+1)). - Alois P. Heinz, Jun 20 2012

Maple

a:= n-> (Matrix(9, (i, j)-> `if`(i=j-1, 1, `if`(i=9,
         [-1, -7, 98, -62, -532, 616, -34, -98, 21][j], 0)))^(n+3).
         <<5, -1, 0, 0, 0, 0, 10, 214, 3491>>)[1, 1]:
seq (a(n), n=0..30);  # Alois P. Heinz, Jun 20 2012

Mathematica

LinearRecurrence[{21, -98, -34, 616, -532, -62, 98, -7, -1}, {0, 0, 0, 10, 214, 3491, 52001, 748788, 10636260}, 30] (* Jean-François Alcover, Feb 17 2016 *)

Prog

(PARI) concat(vector(3), Vec((x^4+2*x^3-23*x^2+4*x+10)*x^3 / ((x-1) * (x^2+14*x-1) * (x^2-2*x-1) * (x^2+2*x-1) * (x^2-6*x+1)) + O(x^30))) \\ Colin Barker, Feb 17 2016

Crossrefs

Cf. A000129, A213785.

Sequence in context: A245985 A309737 A211912 * A278125 A274763 A002967

Adjacent sequences: A213785 A213786 A213787 * A213789 A213790 A213791

Keyword

nonn,easy

Author

N. J. A. Sloane, Jun 20 2012

Status

approved