A155120 a(n) = 2*(n^3 + n^2 + n - 1).
-2, 4, 26, 76, 166, 308, 514, 796, 1166, 1636, 2218, 2924, 3766, 4756, 5906, 7228, 8734, 10436, 12346, 14476, 16838, 19444, 22306, 25436, 28846, 32548, 36554, 40876, 45526, 50516, 55858
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..2000
- Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
Programs
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Magma
[2*(n^3+n^2+n-1): n in [0..40] ]; // Vincenzo Librandi, May 23 2011
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Maple
seq( 2*(n^3 +n^2 +n -1), n=0..40); # G. C. Greubel, Mar 25 2021
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Mathematica
Table[-2 +2n +2n^2 +2n^3, {n, 0, 30}] LinearRecurrence[{4,-6,4,-1},{-2,4,26,76},40] (* Harvey P. Dale, Jun 06 2014 *) -
Sage
[2*(n^3 +n^2 +n -1) for n in (0..40)] # G. C. Greubel, Mar 25 2021
Formula
a(n) = 2*(n^3 +n^2 +n -1).
G.f.: 2*(-1 +6*x -x^2 +2*x^3)/(1-x)^4.
E.g.f.: 2*(-1 + 3*x + 4*x^2 + x^3)*exp(x). - G. C. Greubel, Mar 25 2021