A110003 n followed by n^3 followed by n^2 followed by n^4.

1, 1, 1, 1, 2, 8, 4, 16, 3, 27, 9, 81, 4, 64, 16, 256, 5, 125, 25, 625, 6, 216, 36, 1296, 7, 343, 49, 2401, 8, 512, 64, 4096, 9, 729, 81, 6561, 10, 1000, 100, 10000, 11, 1331, 121, 14641, 12, 1728, 144, 20736, 13, 2197, 169, 28561, 14, 2744, 196, 38416, 15, 3375

Offset: 1

Author

Mohammad K. Azarian, Sep 02 2005

Keywords

• nonn

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).

Crossrefs

Cf. A000463, A109588, A109594.

Programs

Magma

&cat[[n,n^3,n^2,n^4]: n in [1..15]]; // Bruno Berselli, Sep 01 2016

Mathematica

Table[{n, n^3, n^2, n^4}, {n, 1, 15}] // Flatten (* Jean-François Alcover, Sep 01 2016 *)

Formula

a(n) = (2*n+3-(-1)^n+2*(-1)^((2*n+5-(-1)^n)/4))*(n^3+4*n^2+32*n+96+(n^3+4*n^2-64)*(-1)^n-(n^3-4*n^2-64)*(-1)^((2*n+5-(-1)^n)/4)+(n^3-4*n^2-32*n+32)*(-1)^((2*n+7+(-1)^n)/4))/2048. - Luce ETIENNE, Sep 01 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 - 11*x^11 + x^10 + 3*x^9 - 3*x^8 - 11*x^7 + 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)