A000463 -id:A000463 - cp's OEIS frontend

A109815 n^2 followed by n^3 followed by n.

1, 1, 1, 4, 8, 2, 9, 27, 3, 16, 64, 4, 25, 125, 5, 36, 216, 6, 49, 343, 7, 64, 512, 8, 81, 729, 9, 100, 1000, 10, 121, 1331, 11, 144, 1728, 12, 169, 2197, 13, 196, 2744, 14, 225, 3375, 15, 256, 4096, 16, 289, 4913, 17, 324, 5832, 18, 361, 6859, 19, 400, 8000, 20

Offset: 1

Mohammad K. Azarian, Aug 30 2005

Index entries for linear recurrences with constant coefficients, signature (0,0,4,0,0,-6,0,0,4,0,0,-1).

Cf. A000463.

Cf. A010872.

Table[{n^2,n^3,n},{n,20}]//Flatten (* or *) LinearRecurrence[{0,0,4,0,0,-6,0,0,4,0,0,-1},{1,1,1,4,8,2,9,27,3,16,64,4},60] (* Harvey P. Dale, May 26 2018 *)

G.f.: x*(1+x+x^2+4*x^4-2*x^5-x^6+x^7+x^8) / ( (x-1)^4*(1+x+x^2)^4 ). - R. J. Mathar, Mar 03 2014

a(n) = floor((n+2)/3)^((n mod 3)+1). - Luce ETIENNE, Mar 01 2018

A110005 n followed by n^2 followed by n^4 followed by n^3.

Original entry on oeis.org

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

Offset: 1

Mohammad K. Azarian, Sep 02 2005

nonn

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).

Cf. A000463; A109588; A109594.

Cf. A010873.

Table[{n,n^2,n^4,n^3},{n,20}]//Flatten (* Harvey P. Dale, Jan 12 2020 *)

G.f.: x*(-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) / ( (x-1)^5 *(1+x)^5 *(x^2+1)^5 ). - R. J. Mathar, Sep 10 2016

a(n) = floor((n+3)/4)^((-2*(n mod 4)^3 + 15*(n mod 4)^2 -25*(n mod 4) +18)/6). - Luce ETIENNE, Apr 07 2018

A126951 List of pairs: k followed by k^3.

Original entry on oeis.org

1, 1, 2, 8, 3, 27, 4, 64, 5, 125, 6, 216, 7, 343, 8, 512, 9, 729, 10, 1000, 11, 1331, 12, 1728, 13, 2197, 14, 2744, 15, 3375, 16, 4096, 17, 4913, 18, 5832, 19, 6859, 20, 8000, 21, 9261, 22, 10648, 23, 12167, 24, 13824, 25, 15625, 26, 17576, 27, 19683, 28, 21952

Offset: 1

Zak Seidov, Mar 18 2007

nonn

Index entries for linear recurrences with constant coefficients, signature (0, 4, 0, -6, 0, 4, 0, -1).

Cf. A000463, A109588, A109594-5, A109614-6, A110001, A110003-5, A110008-9, A110485, A110622, A110650-3.

&cat[ [ n, n^3 ]: n in [1..40] ]; // Vincenzo Librandi, Apr 21 2011

Table[((((-1)^(n+1))+1)/4)(n+1)- ((((-1)^(n+1))-1)/16)n^3,{n,64}]
Flatten[Table[{n,n^3},{n,30}]] (* or *) LinearRecurrence[{0,4,0,-6,0,4,0,-1},{1,1,2,8,3,27,4,64},60] (* Harvey P. Dale, Mar 11 2018 *)

a(n) = (n+1)/2 if n is odd, a(n) = (n/2)^3 otherwise;
a(n) = ((((-1)^(n+1))+1)/4)*(n+1) - ((((-1)^(n+1))-1)/16)*n^3;
g.f.: (x + x^2 - 2*x^3 + 4*x^4 + x^5 + x^6)/(1 - x^2)^4.

A158613 Expansion of (1 - 2*x^3 - x^4 - x^5 + x^6 + x^7 - x^8)/(1 - x^3)^3.

Original entry on oeis.org

1, 0, 0, 1, -1, -1, 1, -2, -4, 1, -3, -9, 1, -4, -16, 1, -5, -25, 1, -6, -36, 1, -7, -49, 1, -8, -64, 1, -9, -81, 1, -10, -100, 1, -11, -121, 1, -12, -144, 1, -13, -169, 1, -14, -196, 1, -15, -225, 1, -16, -256, 1, -17, -289, 1, -18, -324, 1, -19, -361, 1, -20, -400, 1, -21, -441

Offset: 0

Roger L. Bagula, Mar 22 2009

The sequence is given by the successive triples (1, -m, -m^2) with m = 0, 1, 2, 3, ... - Bruno Berselli, Aug 23 2018

			As array:
1,   0,    0;
1,  -1,   -1;
1,  -2,   -4;
1,  -3,   -9;
1,  -4,  -16;
1,  -5,  -25;
1,  -6,  -36;
1,  -7,  -49;
1,  -8,  -64;
1,  -9,  -81;
1, -10, -100 etc.

Index entries for linear recurrences with constant coefficients, signature (0,0,3,0,0,-3,0,0,1).

Cf. A000463, A156133, A234357.

&cat [[1,-n,-n^2]: n in [0..25]]; // Bruno Berselli, Aug 23 2018

CoefficientList[Series[(1-2x^3-x^4-x^5+x^6+x^7-x^8)/(1-x^3)^3,{x,0,100}],x] (* or *) LinearRecurrence[{0,0,3,0,0,-3,0,0,1},{1,0,0,1,-1,-1,1,-2,-4},100] (* Harvey P. Dale, Nov 22 2021 *)

From Bruno Berselli, Aug 23 2018: (Start)
G.f.: (1 - 2*x^3 - x^4 - x^5 + x^6 + x^7 - x^8)/((1 - x)^3*(1 + x + x^2)^3).
a(n) = 3*a(n-3) - 3*a(n-6) + a(n-9) for n>8.
a(n) = -(-1)^((n+1) mod 3)*floor(n/3)^(n mod 3). (End)

Edited, new name, and a(1)-a(2) added by Bruno Berselli, Aug 23 2018

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A109815 n^2 followed by n^3 followed by n.

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A110005 n followed by n^2 followed by n^4 followed by n^3.

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A126951 List of pairs: k followed by k^3.

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A158613 Expansion of (1 - 2*x^3 - x^4 - x^5 + x^6 + x^7 - x^8)/(1 - x^3)^3.

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