A173433 a(n) = (A000045(n)+A173432(n))/2.

1, 1, 2, 2, 3, 4, 7, 11, 18, 28, 45, 72, 117, 189, 306, 494, 799, 1292, 2091, 3383, 5474, 8856, 14329, 23184, 37513, 60697, 98210, 158906, 257115, 416020, 673135, 1089155, 1762290, 2851444, 4613733, 7465176, 12078909, 19544085, 31622994, 51167078, 82790071, 133957148

Offset: 1

Author

Mark Dols, Feb 18 2010

Keywords

• nonn
• easy

Comments

Also the NW-SE diagonal sums of A173398.

Links

• Robert Israel, Table of n, a(n) for n = 1..4783
• Index entries for linear recurrences with constant coefficients, signature (2,0,-2,2,0,-1).

Crossrefs

Cf. A112468, A000045, A057079, A173432, A173398.

Programs

Maple

f:=gfun:-rectoproc({-a(n) - a(n + 1) + a(n + 2) - a(n + 3) - a(n + 4) + a(n + 5) + 1, a(0) = 0, a(1) = 1, a(2) = 1, a(3) = 2, a(4) = 2, a(5) = 3},a(n),remember):
map(f, [$1..50]); # Robert Israel, Jun 11 2019

Mathematica

CoefficientList[Series[-x*(-1+x+x^4)/((x-1)*(1+x)*(x^2+x-1)*(x^2-x+1)),{x,0,42}],x] (* Georg Fischer, Jun 11 2019 *)

Formula

a(n) = 1/2-(-1)^n/6+A057079(n+4)/6+A000045(n)/2 with g.f. -x*(-1+x+x^4)/ ((x-1) * (1+x) * (x^2+x-1) * (x^2-x+1)). - R. J. Mathar, Mar 04 2010

Extensions

a(35) corrected by Georg Fischer, Jun 11 2019