|
|
A103454
|
|
a(n) = 0^n + 4^n - 1.
|
|
3
|
|
|
1, 3, 15, 63, 255, 1023, 4095, 16383, 65535, 262143, 1048575, 4194303, 16777215, 67108863, 268435455, 1073741823, 4294967295, 17179869183, 68719476735, 274877906943, 1099511627775, 4398046511103, 17592186044415, 70368744177663
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
A transform of 4^n under the matrix A103452.
The square of the cotangent of the arcsin of 1/(2^n). - Al Hakanson (hawkuu(AT)excite.com), Feb 23 2006
|
|
LINKS
|
|
|
FORMULA
|
G.f.: (1 - 2*x + 4*x^2)/((1-x)*(1-4*x));
a(n) = Sum_{k=0..n} A103452(n, k)*4^k;
a(n) = Sum_{k=0..n} (2*0^(n-k) - 1)*0^(k*(n-k))4^k.
|
|
MATHEMATICA
|
Table[Boole[n==0] +4^n -1, {n, 0, 40}] (* G. C. Greubel, Jun 21 2021 *)
|
|
PROG
|
(Sage) [1]+[4^n -1 for n in [1..40]] # G. C. Greubel, Jun 21 2021
|
|
CROSSREFS
|
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|