|
|
A110651
|
|
n^2 followed by n^4 followed by n^3 followed by n.
|
|
1
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,5
|
|
LINKS
|
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
|
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
|
(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
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|