|
| |
|
|
A264147
|
|
a(n) = n*F(n+1) - (n+1)*F(n), where F = A000045.
|
|
1
|
|
|
|
0, -1, 1, 1, 5, 10, 22, 43, 83, 155, 285, 516, 924, 1639, 2885, 5045, 8773, 15182, 26162, 44915, 76855, 131119, 223101, 378696, 641400, 1084175, 1829257, 3081193, 5181893, 8702290, 14594830, 24446971, 40902299, 68359619, 114132765, 190373580, 317258388, 528265207
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,5
|
|
|
COMMENTS
|
a(n) is prime for n = 4, 7, 8, 26, 28, 52, 86, 87, 93, 97, 158, 196, 303, 2908, 3412, 4111, 4208, 6183, 6337, 9878, ...
|
|
|
LINKS
|
Bruno Berselli, Table of n, a(n) for n = 0..500
Index entries for linear recurrences with constant coefficients, signature (2,1,-2,-1).
|
|
|
FORMULA
|
G.f.: x*(-1 + 3*x)/(1 - x - x^2)^2.
a(n) = 2*a(n-1) + a(n-2) - 2*a(n-3) - a(n-4).
a(n) = n*F(n-1) - F(n).
a(n) = Sum_{i=0..n} F(i)*L(n-1-i), where L() is a Lucas number (A000032).
a(n) = 3*A001629(n) - A001629(n+1).
a(n) = -(-1)^n*A178521(-n).
a(n+2) - a(n) = A007502(n+1).
Sum_{i>0} 1/a(i) = 1.39516607051636028893879220294180374...
a(n) = (-((1+sqrt(5))/2)^n*(2*sqrt(5) + (-5+sqrt(5))*n) + ((1-sqrt(5))/2)^n*(2*sqrt(5) + (5+sqrt(5))*n)) / 10. - Colin Barker, Jul 27 2017
|
|
|
MATHEMATICA
|
Table[n Fibonacci[n + 1] - (n + 1) Fibonacci[n], {n, 0, 40}]
|
|
|
PROG
|
(PARI) for(n=0, 40, print1(n*fibonacci(n+1)-(n+1)*fibonacci(n)", "));
(Sage) [n*fibonacci(n+1)-(n+1)*fibonacci(n) for n in (0..40)]
(Maxima) makelist(n*fib(n+1)-(n+1)*fib(n), n, 0, 40);
(MAGMA) [n*Fibonacci(n+1)-(n+1)*Fibonacci(n): n in [0..40]];
(PARI) concat(0, Vec(-x*(1 - 3*x) / (1 - x - x^2)^2 + O(x^50))) \\ Colin Barker, Jul 27 2017
|
|
|
CROSSREFS
|
Cf. A000045, A001629, A007502.
Cf. A178521: n*F(n+1) + (n+1)*F(n).
Cf. A094588: n*F(n-1) + F(n).
Cf. A099920: Sum_{i=0..n} F(i)*L(n-i).
Cf. A023607: Sum_{i=0..n} F(i)*L(n+1-i).
Sequence in context: A271257 A087746 A064694 * A229440 A067622 A196240
Adjacent sequences: A264144 A264145 A264146 * A264148 A264149 A264150
|
|
|
KEYWORD
|
sign,easy
|
|
|
AUTHOR
|
Bruno Berselli, Nov 04 2015
|
|
|
STATUS
|
approved
|
| |
|
|
