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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Partial sums of powers of 256 (A133752), q-integers for q=256.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..400

Quynh Nguyen, Jean Pedersen, and Hien T. Vu, New Integer Sequences Arising From 3-Period Folding Numbers, Vol. 19 (2016), Article 16.3.1. Cites this sequence.

Index entries related to partial sums.

Index entries related to q-numbers.

Index entries for linear recurrences with constant coefficients, signature (257,-256).

FORMULA

a(n) = floor( 256^n/255 ).

G.f.: x/((1-x)*(1-256*x)). - Vincenzo Librandi, Nov 07 2012

a(n) = 257*a(n-1) - 256*a(n-2). - Vincenzo Librandi, Nov 07 2012

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

CROSSREFS

Cf. similar sequences of the form (k^n-1)/(k-1) listed in A269025.

Sequence in context: A125649 A219549 A219548 * A097736 A283510 A103349

Adjacent sequences:  A218720 A218721 A218722 * A218724 A218725 A218726

KEYWORD

nonn,easy

AUTHOR

M. F. Hasler, Nov 04 2012

STATUS

approved

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Last modified February 21 14:40 EST 2018. Contains 299414 sequences. (Running on oeis4.)