A140201 Partial sums of A140081.

0, 1, 2, 4, 4, 5, 6, 8, 8, 9, 10, 12, 12, 13, 14, 16, 16, 17, 18, 20, 20, 21, 22, 24, 24, 25, 26, 28, 28, 29, 30, 32, 32, 33, 34, 36, 36, 37, 38, 40, 40, 41, 42, 44, 44, 45, 46, 48, 48, 49, 50, 52, 52, 53, 54, 56, 56, 57, 58, 60, 60, 61, 62, 64, 64, 65, 66, 68, 68, 69, 70, 72, 72, 73, 74

Offset

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

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

Formula

a(n) = A047624(n+1) - A042948(A004526(n)). - Reinhard Zumkeller, Feb 21 2010

a(n) = A002265(n+1) + A057353(n+1). - Reinhard Zumkeller, Feb 26 2011

From Bruno Berselli, Jan 27 2011: (Start)

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

a(n) = a(n-1) + a(n-4) - a(n-5) for n>4.

a(n) = n + A121262(n+1). (End)

a(n) = n when n+1 is not a multiple of 4, and a(n) = n+1 when n+1 is a multiple of 4. - Dennis P. Walsh, Aug 06 2012

a(n) = A004524(n+1) + A004526(n+1). - Arkadiusz Wesolowski, Sep 17 2012

a(n) = (4*n+1-i^(2*n)+(-i)^(1+n)+i^(1+n))/4 where i=sqrt(-1). - Wesley Ivan Hurt, Jun 04 2016

a(n) = n+1-(sign((n+1) mod 4) mod 3). - Wesley Ivan Hurt, Sep 26 2017

Maple

A140201:=n->(4*n+1-I^(2*n)+(-I)^(1+n)+I^(1+n))/4: seq(A140201(n), n=0..100); # Wesley Ivan Hurt, Jun 04 2016

Mathematica

Accumulate[PadRight[{}, 68, {0, 1, 1, 2}]] (* Harvey P. Dale, Aug 19 2011 *)

Prog

(Magma) I:=[0, 1, 2, 4, 4]; [n le 5 select I[n] else Self(n-1)+Self(n-4)-Self(n-5): n in [1..80]]; // Vincenzo Librandi, Sep 17 2012

Crossrefs

Cf. A002265, A004524, A004526, A042948, A047624, A057353, A121262.

Sequence in context: A295012 A308629 A100921 * A351393 A057861 A133143

Adjacent sequences: A140198 A140199 A140200 * A140202 A140203 A140204

Keyword

easy,nonn

Author

Nadia Heninger and N. J. A. Sloane, Jun 09 2008

Status

approved