A171218 a(n) = Sum_{k=0..n} A109613(k)*A005843(n-k).

0, 2, 6, 16, 32, 58, 94, 144, 208, 290, 390, 512, 656, 826, 1022, 1248, 1504, 1794, 2118, 2480, 2880, 3322, 3806, 4336, 4912, 5538, 6214, 6944, 7728, 8570, 9470, 10432, 11456, 12546, 13702, 14928, 16224, 17594, 19038, 20560, 22160, 23842, 25606

Offset: 0

Author

Reinhard Zumkeller, Dec 05 2009

Keywords

• nonn
• easy

Comments

a(n) is the number of triples (w,x,y) with all terms in {0,...,n} and 2|w-x|Clark Kimberling, Jun 11 2012]

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (3,-2,-2,3,-1).

Programs

Magma

[&+[(2*k+(-1)^k+1)*(n-k): k in [0..n]]: n in [0..42]]; // Bruno Berselli, Nov 16 2011

Mathematica

CoefficientList[Series[2x (1+x^2)/((1+x)(1-x)^4),{x,0,50}],x] (* or *) LinearRecurrence[ {3,-2,-2,3,-1},{0,2,6,16,32},50] (* Harvey P. Dale, Jan 22 2023 *)

Formula

a(n+1) - a(n) = A137928(n+1).

From Bruno Berselli, Nov 16 2011: (Start)

G.f.: 2*x*(1+x^2)/((1+x)*(1-x)^4).

a(n) = 2*A131941(n) = (2*n*(2*n^2+3*n+4)-3*(-1)^n+3)/12.

a(n) = -a(-n-1) = 3*a(n-1)-2*a(n-2)-2*a(n-3)+3*a(n-4)-a(n-5). (End)