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

1,5

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).

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

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 *)

Prog

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

Crossrefs

Cf. A000463, A109588, A109594.

Sequence in context: A328755 A187532 A335353 * A253890 A115054 A228561

Adjacent sequences: A110648 A110649 A110650 * A110652 A110653 A110654

Keyword

nonn,easy

Author

Mohammad K. Azarian, Sep 14 2005

Status

approved