A092899 Expansion of (1+2x+3x^2+6x^3)/((1+x)(1-x)^2).

1, 3, 7, 15, 19, 27, 31, 39, 43, 51, 55, 63, 67, 75, 79, 87, 91, 99, 103, 111, 115, 123, 127, 135, 139, 147, 151, 159, 163, 171, 175, 183, 187, 195, 199, 207, 211, 219, 223, 231, 235, 243, 247, 255, 259, 267, 271, 279, 283, 291, 295, 303, 307, 315, 319, 327, 331

Offset: 0

Author

Paul Barry, Mar 12 2004

Keywords

• easy
• nonn

Comments

mod(A092899(n),4)=1,3,3,3,... = sum{k=0..n, mod(2^k,4)} Partial sums of 1,2,4,8,4,8,4,8....

Links

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

Formula

a(n)=4floor((n+1)/2)+4n-5+6*0^n; a(n)=sum{k=0...n, mod(A078008(k), 4)}+sum{k=0..n, 2*mod(A001045(k), 4)}.

For n > 0, a(n) = 6*n - 4 - (-1)^n; a(n+3) = a(n+2) + a(n+1) - a(n) - Warut Roonguthai, Oct 19 2005