|
|
A350717
|
|
a(n) = 4*a(n-1) - n - 1, for n > 0, a(0) = 1.
|
|
0
|
|
|
1, 2, 5, 16, 59, 230, 913, 3644, 14567, 58258, 233021, 932072, 3728275, 14913086, 59652329, 238609300, 954437183, 3817748714, 15270994837, 61083979328, 244335917291, 977343669142, 3909374676545, 15637498706156, 62549994824599, 250199979298370, 1000799917193453, 4003199668773784
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
Last digit (using 0 to 9) is of period 10: repeat [1, 2, 5, 6, 9, 0, 3, 4, 7, 8].
|
|
LINKS
|
|
|
FORMULA
|
a(n) = (2^(2*n+1) + 3*n + 7)/9.
a(n) = 6*a(n-1) - 9*a(n-2) + 4*a(n-3), n >= 3.
a(n) = -1 + 5*a(n-1) - 4*a(n-2), n >= 2.
|
|
MATHEMATICA
|
LinearRecurrence[{6, -9, 4}, {1, 2, 5}, 28] (* Amiram Eldar, Feb 03 2022 *)
|
|
PROG
|
(PARI) a(n) = if (n, 4*a(n-1) - n - 1, 1); \\ Michel Marcus, Feb 03 2022
(Python)
print([(2**(2*n+1) + 3*n + 7)//9 for n in range(30)])
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|