A086605 a(n) = 9*n^3 - 18*n^2 + 10*n.
0, 1, 20, 111, 328, 725, 1356, 2275, 3536, 5193, 7300, 9911, 13080, 16861, 21308, 26475, 32416, 39185, 46836, 55423, 65000, 75621, 87340, 100211, 114288, 129625, 146276, 164295, 183736, 204653, 227100, 251131, 276800, 304161, 333268, 364175
Offset: 0
Links
- G. C. Greubel, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
Programs
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GAP
List([0..40], n-> n*(1 + 9*(n-1)^2) ); # G. C. Greubel, Feb 08 2020
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Magma
[9*n^3 - 18*n^2 + 10*n: n in [0..40]]; // G. C. Greubel, Feb 08 2020
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Maple
seq( 9*n^3 - 18*n^2 + 10*n, n=0..40); # G. C. Greubel, Feb 08 2020
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Mathematica
Table[9n^3-18n^2+10n,{n,0,40}] (* or *) LinearRecurrence[{4,-6,4,-1},{0,1,20,111},40] (* Harvey P. Dale, Mar 05 2013 *) -
PARI
vector(41, n, my(m=n-1); 9*m^3 - 18*m^2 + 10*m) \\ G. C. Greubel, Feb 08 2020
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Sage
[9*n^3 - 18*n^2 + 10*n for n in (0..40)] # G. C. Greubel, Feb 08 2020
Formula
G.f.: x*(1 + 16*x + 37*x^2)/(1-x)^4.
a(0)=0, a(1)=1, a(2)=20, a(3)=111, a(n)=4*a(n-1)-6*a(n-2)+4*a(n-3)-a(n-4). - Harvey P. Dale, Mar 05 2013
E.g.f.: x*(1 + 9*x + 9*x^2)*exp(x). - G. C. Greubel, Feb 08 2020
Comments