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

0,9

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).

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

Example

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; ...

Mathematica

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

Prog

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

Crossrefs

Cf. A110009.

Sequence in context: A203072 A131873 A220130 * A040059 A178603 A018810

Adjacent sequences: A276068 A276069 A276070 * A276072 A276073 A276074

Keyword

nonn,easy,tabf

Author

Luce ETIENNE, Aug 18 2016

Status

approved