A230196 Number of pairs (p,q) such that 2*p + 3*q = n and p != q.

0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 2, 1, 2, 2, 1, 2, 3, 2, 3, 2, 3, 3, 4, 3, 3, 4, 4, 4, 5, 3, 5, 5, 5, 5, 5, 5, 6, 6, 6, 5, 7, 6, 7, 7, 6, 7, 8, 7, 8, 7, 8, 8, 9, 8, 8, 9, 9, 9, 10, 8, 10, 10, 10, 10, 10, 10, 11, 11, 11, 10, 12, 11, 12, 12, 11, 12, 13, 12, 13, 12, 13, 13, 14, 13, 13, 14, 14, 14, 15, 13, 15, 15, 15, 15, 15, 15, 16, 16, 16

Offset

1,11

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

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

Formula

a(n) = floor((n+1)/6)+floor((n-1)/6)-floor(n/6)+floor((n-1)/5)-floor(n/5).

G.f.: x*(2*x^8 + 2*x^7 + x^6)/((1+x)*(1-x^3)*(1-x^5)). - Ralf Stephan, Oct 12 2013

a(n) = floor((n-3)/2)-floor((n-3)/3)+floor((n-1)/5)-floor(n/5). - Mircea Merca, Nov 27 2013

Maple

seq(floor((n+1)*(1/6))+floor((n-1)*(1/6))-floor((1/6)*n)+floor((n-1)*(1/5))-floor((1/5)*n), n=1..99)

Mathematica

CoefficientList[Series[(2 x^8 + 2 x^7 + x^6)/((1 + x) (1 - x^3) (1 - x^5)), {x, 0, 100}], x] (* Vincenzo Librandi, Oct 13 2013 *)

Prog

(Magma) [Floor((n+1)*(1/6))+Floor((n-1)*(1/6))-Floor((1/6)*n)+Floor((n-1)*(1/5))-Floor((1/5)*n): n in [1..80]]; // Vincenzo Librandi, Oct 13 2013

Crossrefs

Sequence in context: A230241 A029315 A070080 * A131400 A132749 A271106

Adjacent sequences: A230193 A230194 A230195 * A230197 A230198 A230199

Keyword

nonn,easy

Author

Mircea Merca, Oct 11 2013

Status

approved