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

Author

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

Keywords

• easy
• nonn

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).

Crossrefs

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

Programs

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

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 *)

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