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A218723
a(n) = (256^n - 1)/255.
35
0, 1, 257, 65793, 16843009, 4311810305, 1103823438081, 282578800148737, 72340172838076673, 18519084246547628289, 4740885567116192841985, 1213666705181745367548161, 310698676526526814092329217, 79538861190790864407636279553, 20361948464842461288354887565569
OFFSET
0,3
COMMENTS
Partial sums of powers of 256 (A133752), q-integers for q=256.
LINKS
FORMULA
a(n) = floor(256^n/255).
From Vincenzo Librandi, Nov 07 2012: (Start)
G.f.: x/((1 - x)*(1 - 256*x)).
a(n) = 257*a(n-1) - 256*a(n-2). (End)
E.g.f.: exp(x)*(exp(255*x) - 1)/255. - Stefano Spezia, Mar 23 2023
MATHEMATICA
LinearRecurrence[{257, -256}, {0, 1}, 30] (* Vincenzo Librandi, Nov 07 2012 *)
PROG
(PARI) A218723(n)=256^n\255
(Magma) [n le 2 select n-1 else 257*Self(n-1) - 256*Self(n-2): n in [1..20]]; // Vincenzo Librandi, Nov 07 2012
(Python)
def A218723(n): return (1<<(n<<3))//255 # Chai Wah Wu, Nov 10 2022
CROSSREFS
Cf. A133752.
Cf. similar sequences of the form (k^n-1)/(k-1) listed in A269025.
Sequence in context: A219549 A219548 A351865 * A097736 A283510 A103349
KEYWORD
nonn,easy
AUTHOR
M. F. Hasler, Nov 04 2012
STATUS
approved