|
|
A152417
|
|
a(n) = (5^n - 1)/(2^(3 - (n mod 2))).
|
|
1
|
|
|
0, 1, 3, 31, 78, 781, 1953, 19531, 48828, 488281, 1220703, 12207031, 30517578, 305175781, 762939453, 7629394531, 19073486328, 190734863281, 476837158203, 4768371582031, 11920928955078, 119209289550781, 298023223876953, 2980232238769531, 7450580596923828
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
LINKS
|
|
|
FORMULA
|
a(n) = (5^n - 1)/(2^(3 - (n mod 2))).
a(n) = (5^n-1)/8 for n even.
a(n) = (5^n-1)/4 for n odd.
a(n) = 26*a(n-2)-25*a(n-4) for n>3.
G.f.: x*(5*x^2+3*x+1) / ((x-1)*(x+1)*(5*x-1)*(5*x+1)).
(End)
|
|
MATHEMATICA
|
a[n_] := (5^n - 1)/(2^(3 - Mod[n, 2]));
Table[a[n], {n, 0, 30}]
LinearRecurrence[{0, 26, 0, -25}, {0, 1, 3, 31}, 30] (* Harvey P. Dale, Aug 05 2018 *)
|
|
PROG
|
(PARI) concat(0, Vec(x*(5*x^2+3*x+1) / ((x-1)*(x+1)*(5*x-1)*(5*x+1)) + O(x^30))) \\ Colin Barker, Nov 16 2015
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|