A110622 n^2 followed by n followed by n^3 followed by n^4.
1, 1, 1, 1, 4, 2, 8, 16, 9, 3, 27, 81, 16, 4, 64, 256, 25, 5, 125, 625, 36, 6, 216, 1296, 49, 7, 343, 2401, 64, 8, 512, 4096, 81, 9, 729, 6561, 100, 10, 1000, 10000, 121, 11, 1331, 14641, 144, 12, 1728, 20736, 169, 13, 2197, 28561, 196, 14, 2744, 38416, 225, 15
Offset: 1
Links
- Vincenzo Librandi, Table of n, a(n) for n = 1..8000
- Index entries for linear recurrences with constant coefficients, signature (0,0,0,5,0,0,0,-10,0,0,0,10,0,0,0,-5,0,0,0,1).
Programs
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Magma
&cat[[n^2, n, n^3, n^4]: n in [1..20]]; // Vincenzo Librandi, Nov 25 2012
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Mathematica
Flatten[Table[{n^2, n, n^3, n^4}, {n, 40}]] (* Vincenzo Librandi, Nov 25 2012 *) -
PARI
lista(nn) = for(n=1, nn, print1(n^2, ", ", n, ", ", n^3, ", "n^4, ", ")); \\ Jinyuan Wang, Feb 28 2020
Formula
a(n) = 5*a(n-4) - 10*a(n-8) + 10*a(n-12) - 5*a(n-16) + a(n-20).
G.f.: -x*(1 + x + x^2 + x^3 - x^4 - 3*x^5 + 3*x^6 + 11*x^7 - x^8 + 3*x^9 - 3*x^10 + 11*x^11 + x^12 - x^13 - x^14 + x^15) / ( (x-1)^5*(1+x)^5*(x^2+1)^5 ). - R. J. Mathar, Dec 20 2010
a(n) = (2*n + 3 - (-1)^n + 2*(-1)^((2*n + 5 - (-1)^n)/4))*(n^3 + 4*n^2 + 24*n + 116 + (n^3 - 4*n^2 - 24*n + 12)*(-1)^n - (n^3 + 4*n^2 - 8*n - 108)*(-1)^((2*n + 5 - (-1)^n)/4) + (n^3 - 4*n^2 + 8*n - 20)*(-1)^((2*n + 7 + (-1)^n)/4))/2048. - Luce ETIENNE, Sep 02 2016