A110652 n^2 followed by n^3 followed by n^4 followed by n.
1, 1, 1, 1, 4, 8, 16, 2, 9, 27, 81, 3, 16, 64, 256, 4, 25, 125, 625, 5, 36, 216, 1296, 6, 49, 343, 2401, 7, 64, 512, 4096, 8, 81, 729, 6561, 9, 100, 1000, 10000, 10, 121, 1331, 14641, 11, 144, 1728, 20736, 12, 169, 2197, 28561, 13, 196, 2744, 38416, 14, 225
Offset: 1
Links
- Vincenzo Librandi, Table of n, a(n) for n = 1..4000
- 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^3, n^4, n]: n in [1..20]]; // Vincenzo Librandi, Feb 06 2013
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Mathematica
Flatten[Table[{n^2, n^3, n^4, n}, {n, 40}]] (* Vincenzo Librandi, Feb 06 2013 *) -
PARI
Vec(x*(1+x+x^2+x^3-x^4+3*x^5+11*x^6-3*x^7-x^8-3*x^9+11*x^10+3*x^11+x^12-x^13+x^14-x^15) / ((1-x)^5*(1+x)^5*(1+x^2)^5) + O(x^20)) \\ Colin Barker, Aug 18 2016
Formula
a(n) = (2*n+3-(-1)^n+2*(-1)^((2*n+5-(-1)^n)/4))*(n^3+7*n^2+35*n+129-(n^3-n^2+3*n-31)*(-1)^n-(n^3-n^2-29*n+1)*(-1)^((2*n+5-(-1)^n)/4)-(n^3+7*n^2+3*n-95)*(-1)^((2*n+7+(-1)^n)/4))/2048. - Luce ETIENNE, Aug 17 2016
G.f.: x*(1+x+x^2+x^3-x^4+3*x^5+11*x^6-3*x^7-x^8-3*x^9+11*x^10+3*x^11+x^12-x^13+x^14-x^15) / ((1-x)^5*(1+x)^5*(1+x^2)^5). - Colin Barker, Aug 18 2016