A110008 n followed by n^4 followed by n^3 followed by n^2.
1, 1, 1, 1, 2, 16, 8, 4, 3, 81, 27, 9, 4, 256, 64, 16, 5, 625, 125, 25, 6, 1296, 216, 36, 7, 2401, 343, 49, 8, 4096, 512, 64, 9, 6561, 729, 81, 10, 10000, 1000, 100, 11, 14641, 1331, 121, 12, 20736, 1728, 144, 13, 28561, 2197, 169, 14, 38416, 2744, 196, 15
Offset: 1
Links
- 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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Mathematica
Flatten[Table[{n,n^Range[4,2,-1]},{n,15}]] (* Harvey P. Dale, Aug 11 2011 *) -
PARI
s=[]; for(n=1, 100, s=concat(s, [n,n^4,n^3,n^2])); s \\ Colin Barker, Dec 13 2014
Formula
G.f.: -x*(x^15-x^14+x^13-x^12-x^11-3*x^10+11*x^9+3*x^8-x^7+3*x^6+11*x^5-3*x^4+x^3+x^2+x+1) / ((x-1)^5*(x+1)^5*(x^2+1)^5). - Colin Barker, Dec 13 2014
a(n) = (2*n+3-(-1)^n+2*(-1)^((2*n+5-(-1)^n)/4))*(n^3+10*n^2+36*n+76+(n^3+2*n^2+20*n-60)*(-1)^n+(n^3+2*n^2-12*n+68)*(-1)^((2*n+5-(-1)^n)/4)-(n^3+10*n^2+4*n-52)*(-1)^((2*n+7+(-1)^n)/4))/2048. - Luce ETIENNE, Aug 27 2016