A110004 n followed by n^3 followed by n^4 followed by n^2.

1, 1, 1, 1, 2, 8, 16, 4, 3, 27, 81, 9, 4, 64, 256, 16, 5, 125, 625, 25, 6, 216, 1296, 36, 7, 343, 2401, 49, 8, 512, 4096, 64, 9, 729, 6561, 81, 10, 1000, 10000, 100, 11, 1331, 14641, 121, 12, 1728, 20736, 144, 13, 2197, 28561, 169, 14, 2744, 38416, 196, 15

Offset: 1

Author

Mohammad K. Azarian, Sep 02 2005

Keywords

• nonn

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).

Crossrefs

Cf. A000463, A109588, A109594.

Programs

Magma

[&cat[[n,n^3,n^4,n^2]: n in [1..20]]]; // Vincenzo Librandi, Sep 05 2016

Mathematica

Table[n^{1, 3, 4, 2}, {n, 15}] // Flatten (* or *)
Table[(2 n + 3 - (-1)^n + 2 (-1)^((2 n + 5 - (-1)^n)/4)) (n^3 + 7 n^2 + 35 n + 81 - (n^3 - n^2 - 29 n + 49) (-1)^n - (n^3 - n^2 + 3 n - 79) (-1)^((2 n + 5 - (-1)^n)/4) - (n^3 + 7 n^2 + 3 n - 47) (-1)^((2 n + 7 + (-1)^n)/4))/2048, {n, 57}] (* Michael De Vlieger, Sep 03 2016 *)
LinearRecurrence[{0,0,0,5,0,0,0,-10,0,0,0,10,0,0,0,-5,0,0,0,1},{1,1,1,1,2,8,16,4,3,27,81,9,4,64,256,16,5,125,625,25},60] (* Harvey P. Dale, Jul 19 2024 *)

Formula

a(n) = (2*n+3-(-1)^n+2*(-1)^((2*n+5-(-1)^n)/4))*(n^3+7*n^2+35*n+81-(n^3-n^2-29*n+49)*(-1)^n-(n^3-n^2+3*n-79)*(-1)^((2*n+5-(-1)^n)/4)-(n^3+7*n^2+3*n-47)*(-1)^((2*n+7+(-1)^n)/4))/2048. - Luce ETIENNE, Sep 03 2016

From Chai Wah Wu, Jan 11 2020: (Start)

a(n) = 5*a(n-4) - 10*a(n-8) + 10*a(n-12) - 5*a(n-16) + a(n-20) for n > 20.

G.f.: x*(-x^15 - x^14 + x^13 + x^12 + x^11 - 11*x^10 + 3*x^9 - 3*x^8 + x^7 - 11*x^6 - 3*x^5 + 3*x^4 - x^3 - x^2 - x - 1)/((x - 1)^5*(x + 1)^5*(x^2 + 1)^5). (End)