A164965 Cumulative sums of A010892.

1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0

Offset

0,2

Links

Table of n, a(n) for n=0..83.

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

Formula

G.f.: 1/((1 - x)*(1 - x + x^2)). - Philippe Deléham, Oct 11 2011

a(n) = a(n-1) - a(n-2) + 1. - Arkadiusz Wesolowski, Jun 08 2013

a(n) = -floor((n - 4)/6) - floor((n - 3)/6) + floor((n - 1)/6) + floor(n/6). - John M. Campbell, Dec 23 2016

E.g.f.: cosh(x) + 2*exp(x/2)*sin(sqrt(3)*x/2)/sqrt(3) + sinh(x). - Stefano Spezia, Feb 20 2023

Mathematica

Table[-Floor[1/6 (-4 + n)] - Floor[1/6 (-3 + n)] + Floor[1/6 (-1 + n)] + Floor[n/6], {n, 0, 100}] (* John M. Campbell, Dec 23 2016 *)
LinearRecurrence[{2, -2, 1}, {1, 2, 2}, 100] (* Harvey P. Dale, Jul 17 2020 *)

Crossrefs

Cf. A010892, A021823, A164925, A108299.

Sequence in context: A024712 A281497 A198243 * A021823 A131026 A333839

Adjacent sequences: A164962 A164963 A164964 * A164966 A164967 A164968

Keyword

easy,nonn

Author

Mark Dols, Sep 02 2009

Extensions

Offset corrected by John M. Campbell, Dec 23 2016

Status

approved