A094025 Expansion of (1+3x)/((1-x^2)(1-3x^2)).

1, 3, 4, 12, 13, 39, 40, 120, 121, 363, 364, 1092, 1093, 3279, 3280, 9840, 9841, 29523, 29524, 88572, 88573, 265719, 265720, 797160, 797161, 2391483, 2391484, 7174452, 7174453, 21523359, 21523360, 64570080, 64570081, 193710243, 193710244

Offset: 0

Author

Paul Barry, Apr 22 2004

Keywords

• easy
• nonn

Comments

Add 1, triple, add 1, triple, ... (of course this is simply a restatement of one of Philippe Deléham's formulas). - Jon Perry, Aug 11 2014

Links

• Index entries for linear recurrences with constant coefficients, signature (0,4,0,-3).

Crossrefs

Cf. A075427, A080610, A083416.

Formula

a(n)=4a(n-2)-3a(n-4); a(n)=3*3^(n/2)(1/4+sqrt(3)/4+(1/4-sqrt(3)/4)(-1)^n)+(-1)^n/2-1.

a(n) = a(n-1)*3 if n odd; a(n) = a(n-1)+1 if n even. - Philippe Deléham, Apr 22 2013

a(2n) = A003462(n+1); a(2n+1) = A123109(n+1) = A029858(n+1). - Philippe Deléham, Apr 22 2013