A141530 a(n) = 4*n^3 - 6*n^2 + 1.
1, -1, 9, 55, 161, 351, 649, 1079, 1665, 2431, 3401, 4599, 6049, 7775, 9801, 12151, 14849, 17919, 21385, 25271, 29601, 34399, 39689, 45495, 51841, 58751, 66249, 74359, 83105, 92511, 102601, 113399, 124929, 137215, 150281, 164151, 178849, 194399, 210825, 228151
Offset: 0
Links
- G. C. Greubel, Table of n, a(n) for n = 0..500
- Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
Programs
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Magma
[4*n^3 -6*n^2 +1: n in [0..50]]; // G. C. Greubel, Mar 29 2021
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Maple
A141530:= n-> 4*n^3 -6*n^2 +1; seq(A141530(n), n=0..50); # G. C. Greubel, Mar 29 2021
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Mathematica
Array[4*#^3-6*#^2+1&,50,0] (* Vladimir Joseph Stephan Orlovsky, Nov 03 2009 *) LinearRecurrence[{4,-6,4,-1},{1,-1,9,55},50] (* Harvey P. Dale, Nov 30 2011 *)
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PARI
a(n)=4*n^3-6*n^2+1 \\ Charles R Greathouse IV, Oct 07 2015
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Python
def A141530(n): return (m:=(n<<1)-1)*(n*(m-1)-1) # Chai Wah Wu, Mar 11 2024
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Sage
[4*n^3 -6*n^2 +1 for n in (0..50)] # G. C. Greubel, Mar 29 2021
Formula
G.f.: (1 - 5*x + 19*x^2 + 9*x^3)/(1-x)^4. - Jaume Oliver Lafont, Aug 30 2009
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) with a(0)=1, a(1)=-1, a(2)=9, a(3)=55. - Harvey P. Dale, Nov 30 2011
E.g.f.: (1 - 2*x + 6*x^2 + 4*x^3)*exp(x). - G. C. Greubel, Mar 29 2021
Extensions
Corrected, completed and edited, following an observation from Vincenzo Librandi, by M. F. Hasler, Feb 12 2009
Further edited by N. J. A. Sloane, Feb 13 2009