A034324 a(n) = (n-1)*(n-2)*(n-3) + n.
1, 2, 3, 10, 29, 66, 127, 218, 345, 514, 731, 1002, 1333, 1730, 2199, 2746, 3377, 4098, 4915, 5834, 6861, 8002, 9263, 10650, 12169, 13826, 15627, 17578, 19685, 21954, 24391, 27002, 29793, 32770, 35939, 39306, 42877, 46658, 50655, 54874, 59321
Offset: 1
Links
- Vincenzo Librandi, Table of n, a(n) for n = 1..1000
- Dorin Andrica and Ovidiu Bagdasar, On k-partitions of multisets with equal sums, The Ramanujan J. (2021) Vol. 55, 421-435.
- Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
Programs
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GAP
List([1..50], n-> (n-2)^3 +2); # G. C. Greubel, Aug 23 2019
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Magma
[(n-2)^3 +2: n in [1..50]]; // G. C. Greubel, Aug 23 2019
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Maple
seq( (n-2)^3 +2, n=1..50); # G. C. Greubel, Aug 23 2019
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Mathematica
Table[(n-3)(n-2)(n-1)+n, {n,50}] (* or *) Table[n^3+2, {n,-1,50}] (* Vladimir Joseph Stephan Orlovsky, Apr 15 2011 *) CoefficientList[Series[(1 -2x +x^2 +6x^3)/(1-x)^4, {x, 0, 50}], x] (* Vincenzo Librandi, Feb 24 2014 *) LinearRecurrence[{4,-6,4,-1},{1,2,3,10},50] (* Harvey P. Dale, Aug 06 2018 *) -
PARI
a(n)=(n-3)*(n-2)*(n-1)+n \\ Charles R Greathouse IV, Jul 02 2016
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Sage
[(n-2)^3 +2 for n in (1..50)] # G. C. Greubel, Aug 23 2019
Formula
a(n) = (n-2)^3 + 2 = A084380(n-2). - Philippe Deléham, Feb 23 2014
a(n+1) = A002061(n)*(n-2) + 3. - Philippe Deléham, Feb 23 2014
G.f.: x*(1-2*x+x^2+6*x^3)/(1-x)^4. - Philippe Deléham, Feb 23 2014
E.g.f.: 6 + (x^3-3*x^2+7*x-6)*exp(x). - Nikolaos Pantelidis, Feb 06 2023
Extensions
Extended and corrected by Erich Friedman
Comments