A100152 Structured truncated cubic numbers.
1, 24, 100, 260, 535, 956, 1554, 2360, 3405, 4720, 6336, 8284, 10595, 13300, 16430, 20016, 24089, 28680, 33820, 39540, 45871, 52844, 60490, 68840, 77925, 87776, 98424, 109900, 122235, 135460, 149606, 164704
Offset: 1
Links
- Vincenzo Librandi, Table of n, a(n) for n = 1..5000
- Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
Crossrefs
Programs
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Magma
[(1/6)*(31*n^3-27*n^2+2*n): n in [1..40]]; // Vincenzo Librandi, Jul 19 2011
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Mathematica
Table[n/6 (31n^2-27n+2),{n,40}] (* or *) LinearRecurrence[{4,-6,4,-1},{1,24,100,260},40] (* Harvey P. Dale, Jan 11 2016 *) -
PARI
vector(50, n, (31*n^3-27*n^2+2*n)/6) \\ G. C. Greubel, Oct 18 2018
Formula
a(n) = (1/6)*n*(31*n^2 - 27*n + 2).
G.f.: x*(1 + 20*x + 10*x^2)/(1-x)^4. - Colin Barker, Jan 19 2012
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4); a(1)=1, a(2)=24, a(3)=100, a(4)=260. - Harvey P. Dale, Jan 11 2016
E.g.f.: x*(6 + 66*x + 31*x^2)*exp(x)/6. - G. C. Greubel, Oct 18 2018