A224521 Numbers a(n) with property a(n) + a(n+5) = 2^(n+5) - 1 = A000225(n+5).

0, 1, 3, 7, 15, 31, 62, 124, 248, 496, 992, 1985, 3971, 7943, 15887, 31775, 63550, 127100, 254200, 508400, 1016800, 2033601, 4067203, 8134407, 16268815, 32537631, 65075262, 130150524, 260301048, 520602096, 1041204192, 2082408385, 4164816771, 8329633543

Offset

0,3

Comments

This is the case k=5 of a(n) + a(n+k) = 2^(n+k) - 1 = A000225(n+k). The sequences A000975, A077854, A153234 and A224520 correspond to cases k=1,2,3 and 4, respectively.

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (3,-2,0,0,-1,3,-2).

Formula

a(n) + a(n+5) = 2^(n+5) - 1.

From Joerg Arndt, Apr 09 2013: (Start)

G.f.: x/((1-x)*(1+x)*(1-2*x)*(1-x+x^2-x^3+x^4)).

a(n) = +3*a(n-1) -2*a(n-2) -1*a(n-5) +3*a(n-6) -2*a(n-7). (End)

a(n) = floor(2^(n+5)/33). - Karl V. Keller, Jr., Jul 03 2021

Mathematica

CoefficientList[Series[x/((1-x)*(1-2*x)*(1+x^5)), {x, 0, 40}], x] (* G. C. Greubel, Oct 11 2017 *)
LinearRecurrence[{3, -2, 0, 0, -1, 3, -2}, {0, 1, 3, 7, 15, 31, 62}, 40] (* Harvey P. Dale, Apr 29 2020 *)

Prog

(PARI) my(x='x+O('x^40)); concat([0], Vec(x/((1-x)*(1-2*x)*(1+x^5)))) \\ G. C. Greubel, Oct 11 2017
(Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( x/((1-x)*(1-2*x)*(1+x^5)) )); // G. C. Greubel, Jun 06 2019
(Sage) (x/((1-x)*(1-2*x)*(1+x^5))).series(x, 40).coefficients(x, sparse=False) # G. C. Greubel, Jun 06 2019
(Python) print([2**(n+5)//33 for n in range(31)]) # Karl V. Keller, Jr., Jul 03 2021

Crossrefs

Cf. A000975, A077854, A153234, A224520.

Sequence in context: A057703 A006739 A119407 * A269167 A261586 A043734

Adjacent sequences: A224518 A224519 A224520 * A224522 A224523 A224524

Keyword

nonn,easy

Author

Arie Bos, Apr 09 2013

Status

approved