A110651 n^2 followed by n^4 followed by n^3 followed by n.

1, 1, 1, 1, 4, 16, 8, 2, 9, 81, 27, 3, 16, 256, 64, 4, 25, 625, 125, 5, 36, 1296, 216, 6, 49, 2401, 343, 7, 64, 4096, 512, 8, 81, 6561, 729, 9, 100, 10000, 1000, 10, 121, 14641, 1331, 11, 144, 20736, 1728, 12, 169, 28561, 2197, 13, 196, 38416, 2744, 14, 225

Offset: 1

Author

Mohammad K. Azarian, Sep 14 2005

Keywords

• nonn
• easy

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^2, n^4, n^3, n]: n in [1..20]]; // Vincenzo Librandi, Feb 06 2013

Mathematica

Flatten[Table[{n^2, n^4, n^3, n}, {n, 40}]](* Vincenzo Librandi, Feb 06 2013 *)
LinearRecurrence[{0,0,0,5,0,0,0,-10,0,0,0,10,0,0,0,-5,0,0,0,1},{1,1,1,1,4,16,8,2,9,81,27,3,16,256,64,4,25,625,125,5},60] (* Harvey P. Dale, Sep 20 2023 *)

PARI

Vec(x*(1+x+x^2+x^3-x^4+11*x^5+3*x^6-3*x^7-x^8+11*x^9-3*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^30)) \\ Colin Barker, Sep 02 2016

Formula

a(n) = (2*n+3-(-1)^n+2*(-1)^((2*n+5-(-1)^n)/4))*(n^3+10*n^2+36*n+124+(n^3+2*n^2-12*n+20)*(-1)^n+(n^3+2*n^2+20*n-12)*(-1)^((2*n+5-(-1)^n)/4)-(n^3+10*n^2+4*n-100)*(-1)^((2*n+7+(-1)^n)/4))/2048. - Luce ETIENNE, Sep 02 2016

G.f.: x*(1+x+x^2+x^3-x^4+11*x^5+3*x^6-3*x^7-x^8+11*x^9-3*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, Sep 02 2016

a(n) = 5*a(n-4)-10*a(n-8)+10*a(n-12)-5*a(n-16)+a(n-20). - Wesley Ivan Hurt, Jun 09 2023