A174679 a(4n) = n^2. a(4n+1) = (4n-1)^2. a(4n+2) = (2n)^2. a(4n+3) = (4n+1)^2.

0, 1, 0, 1, 1, 9, 4, 25, 4, 49, 16, 81, 9, 121, 36, 169, 16, 225, 64, 289, 25, 361, 100, 441, 36, 529, 144, 625, 49, 729, 196, 841, 64, 961, 256, 1089, 81, 1225, 324, 1369, 100, 1521, 400, 1681, 121, 1849, 484, 2025, 144, 2209, 576

Offset: 0

Author

Paul Curtz, Nov 30 2010

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (0,0,0,3,0,0,0,-3,0,0,0,1).

Programs

Mathematica

LinearRecurrence[{0,0,0,3,0,0,0,-3,0,0,0,1},{0,1,0,1,1,9,4,25,4,49,16,81},80] (* Harvey P. Dale, Apr 01 2018 *)

Formula

a(2n) = A174595(n).

a(2n+1) = A016754(n-1) = (2n-1)^2, n>0.

a(4n+1) = A016838(n-1).

a(4n+2) = A016742(n).

a(4n+3) = A016814(n).

a(n)= +3*a(n-4) -3*a(n-8) +a(n-12).

G.f.: -x*(1+x^2+x^3+6*x^4+4*x^5+22*x^6+x^7+25*x^8+4*x^9+9*x^10) / ( (x-1)^3*(1+x)^3*(x^2+1)^3 ). - R. J. Mathar, Dec 01 2010

a(n) = ((16-(1+(-1)^n)*(5+i^n))*n-4*(8-(1+(-1)^n)*(3+i^n)))^2/256, where i=sqrt(-1). - Bruno Berselli, Jan 27 2011 - Apr 09 2011