A276071 n^3 followed by n^2 followed by n^4 followed by n.

0, 0, 0, 0, 1, 1, 1, 1, 8, 4, 16, 2, 27, 9, 81, 3, 64, 16, 256, 4, 125, 25, 625, 5, 216, 36, 1296, 6, 343, 49, 2401, 7, 512, 64, 4096, 8, 729, 81, 6561, 9, 1000, 100, 10000, 10, 1331, 121, 14641, 11, 1728, 144, 20736, 12, 2197, 169, 28561, 13, 2744, 196, 38416, 14, 3375, 225, 50625, 15

Offset: 0

Author

Luce ETIENNE, Aug 18 2016

Keywords

• nonn
• easy
• tabf

Examples

			Rectangular array with four columns begins:
.   0,  0,    0, 0;
.   1,  1,    1, 1;
.   8,  4,   16, 2;
.  27,  9,   81, 3;
.  64, 16,  256, 4;
. 125, 25,  625, 5;
. 216, 36, 1296, 6; ...
		

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• 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. A110009.

Programs

Magma

&cat[[n^3,n^2,n^4,n]: n in [0..20]]; // Bruno Berselli, Aug 21 2016

Mathematica

Flatten[Table[{n^3, n^2, n^4, n}, {n, 0, 20}]] (* Bruno Berselli, Aug 21 2016 *)

PARI

concat(vector(4), Vec(x^4*(1+x+x^2+x^3+3*x^4-x^5+11*x^6-3*x^7-3*x^8-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^60))) \\ Colin Barker, Aug 18 2016

Formula

a(n) = (2*n - 3 + (-1)^n + 2*(-1)^((2*n - 1 + (-1)^n)/4))*(n^3 - 2*n^2 + 28*n + 40 + (n^3 - 2*n^2 - 4*n - 56)*(-1)^n - (n^3 - 10*n^2 - 4*n + 72)*(-1)^((2*n - 1 + (-1)^n)/4) - (n^3 - 10*n^2 + 28*n - 88)*(-1)^((2*n + 1 - (-1)^n)/4))/2048.

G.f.: x^4*(1 + x + x^2 + x^3 + 3*x^4 - x^5 + 11*x^6 - 3*x^7 - 3*x^8 - 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