A152731 a(n) + a(n+1) + a(n+2) = n^6, a(1)=a(2)=0.
0, 0, 1, 63, 665, 3368, 11592, 31696, 74361, 156087, 300993, 542920, 927648, 1515416, 2383745, 3630375, 5376505, 7770336, 10990728, 15251160, 20803993, 27944847, 37017281, 48417776, 62600832, 80084368, 101455425, 127375983
Offset: 1
Keywords
Links
- G. C. Greubel, Table of n, a(n) for n = 1..5000
- Index entries for linear recurrences with constant coefficients, signature (6,-15,21,-21,21,-21,15,-6,1).
Programs
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Magma
m:=30; R
:=PowerSeriesRing(Integers(), m); [0,0] cat Coefficients(R!(x^3*(1+x)*(x^4+56*x^3+246*x^2+56*x+1)/((1-x)^7*(1 +x+ x^2)))); // G. C. Greubel, Sep 01 2018 -
Mathematica
k0=k1=0;lst={k0,k1};Do[kt=k1;k1=n^6-k1-k0;k0=kt;AppendTo[lst,k1],{n,1,5!}];lst LinearRecurrence[{6, -15, 21, -21, 21, -21, 15, -6, 1}, {0, 0, 1, 63, 665, 3368, 11592, 31696, 74361}, 5000] CoefficientList[Series[x^2*(1+x)*(x^4 + 56*x^3 + 246*x^2 + 56*x + 1)/((1-x)^7*(1+x+x^2)),{x, 0, 5000}], x] (* Stefano Spezia, Sep 02 2018 *) -
PARI
x='x+O('x^30); concat([0,0], Vec(x^3*(1+x)*(x^4+56*x^3 +246*x^2 +56*x+1)/((1-x)^7*(1+x+x^2)))) \\ G. C. Greubel, Sep 01 2018
Formula
From R. J. Mathar, Dec 12 2008: (Start)
a(n) = -26*n/3 + 20*n^3/3 - 5*n^2 + 7/3 - 2*n^5 + n^6/3 + 5*n^4/3 - 7*A131713(n)/3.
G.f.: x^3*(1+x)*(x^4 + 56*x^3 + 246*x^2 + 56*x + 1)/((1-x)^7*(1+x+x^2)). (End)
Comments