A110652 n^2 followed by n^3 followed by n^4 followed by n.

1, 1, 1, 1, 4, 8, 16, 2, 9, 27, 81, 3, 16, 64, 256, 4, 25, 125, 625, 5, 36, 216, 1296, 6, 49, 343, 2401, 7, 64, 512, 4096, 8, 81, 729, 6561, 9, 100, 1000, 10000, 10, 121, 1331, 14641, 11, 144, 1728, 20736, 12, 169, 2197, 28561, 13, 196, 2744, 38416, 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+7*n^2+35*n+129-(n^3-n^2+3*n-31)*(-1)^n-(n^3-n^2-29*n+1)*(-1)^((2*n+5-(-1)^n)/4)-(n^3+7*n^2+3*n-95)*(-1)^((2*n+7+(-1)^n)/4))/2048. - Luce ETIENNE, Aug 17 2016

G.f.: x*(1+x+x^2+x^3-x^4+3*x^5+11*x^6-3*x^7-x^8-3*x^9+11*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, Aug 18 2016

Mathematica

Flatten[Table[{n^2, n^3, n^4, n}, {n, 40}]] (* Vincenzo Librandi, Feb 06 2013 *)

Prog

(Magma) &cat[[n^2, n^3, n^4, n]: n in [1..20]]; // Vincenzo Librandi, Feb 06 2013
(PARI) Vec(x*(1+x+x^2+x^3-x^4+3*x^5+11*x^6-3*x^7-x^8-3*x^9+11*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^20)) \\ Colin Barker, Aug 18 2016

Crossrefs

Cf. A000463, A109588, A109594.

Sequence in context: A111988 A361667 A361664 * A354778 A059373 A137798

Adjacent sequences: A110649 A110650 A110651 * A110653 A110654 A110655

Keyword

nonn,easy

Author

Mohammad K. Azarian, Sep 14 2005

Status

approved