A134633 5*n^5 + 3*n^3 + 2*n^2. Coefficients and exponents are the prime numbers in decreasing order.
0, 10, 192, 1314, 5344, 16050, 39600, 85162, 165504, 297594, 503200, 809490, 1249632, 1863394, 2697744, 3807450, 5255680, 7114602, 9465984, 12401794, 16024800, 20449170, 25801072, 32219274, 39855744, 48876250, 59460960, 71805042, 86119264, 102630594, 121582800, 143237050, 167872512, 195786954, 227297344
Offset: 0
Examples
a(4)=5344 because 4^5=1024, 5*1024=5120, 4^3=64, 3*64=192, 4^2=16, 2*16=32 and we can write 5120+192+32=5344.
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (6, -15, 20, -15, 6, -1).
Programs
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Magma
[5*n^5+3*n^3+2*n^2: n in [0..50]]; // Vincenzo Librandi, Dec 14 2010
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Maple
A134633:=n->5*n^5 + 3*n^3 + 2*n^2; seq(A134633(n), n=0..50); # Wesley Ivan Hurt, May 21 2014
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Mathematica
Table[5n^5+3n^3+2n^2,{n,0,40}] (* or *) LinearRecurrence[ {6,-15,20,-15,6,-1},{0,10,192,1314,5344,16050},40] (* Harvey P. Dale, Apr 25 2012 *) CoefficientList[Series[2 x (5 + 66 x + 156 x^2 + 70 x^3 + 3x^4)/(1 - x)^6, {x, 0, 50}], x] (* Vincenzo Librandi, May 21 2014 *)
Formula
a(n) = 5*n^5 + 3*n^3 + 2*n^2.
G.f.: 2x*(5+66x+156x^2+70x^3+3x^4)/(1-x)^6. - R. J. Mathar, Nov 14 2007
a(0)=0, a(1)=10, a(2)=192, a(3)=1314, a(4)=5344, a(5)=16050, a(n)= 6*a(n-1)- 15*a(n-2)+20*a(n-3)-15*a(n-4)+6*a(n-5)-a(n-6). - Harvey P. Dale, Apr 25 2012
Extensions
More terms from Vincenzo Librandi, Dec 14 2010