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A192803
Coefficient of x^2 in the reduction of the polynomial (x+2)^n by x^3->x^2+x+1.
2
0, 0, 1, 7, 34, 144, 575, 2239, 8632, 33164, 127297, 488571, 1875346, 7199124, 27637959, 106107659, 407374592, 1564024808, 6004739025, 23053921567, 88510638482, 339817775144, 1304657986015, 5008956298247, 19230819824088, 73832632141076
OFFSET
0,4
COMMENTS
For discussions of polynomial reduction, see A192232 and A192744.
FORMULA
a(n) = 7*a(n-1)-15*a(n-2)+11*a(n-3).
G.f.: -x^2/(11*x^3-15*x^2+7*x-1). [Colin Barker, Jul 27 2012]
EXAMPLE
The first five polynomials p(n,x) and their reductions:
p(1,x)=1 -> 1
p(2,x)=x+2 -> x+2
p(3,x)=x^2+4x+4 -> x^2+1
p(4,x)=x^3+6x^2+12x+8 -> x^2+4x+4
p(5,x)=x^4+8x^3+24x^2+32x+16 -> 7x^2+13*x+9, so that
A192798=(1,2,4,9,25,...), A192799=(0,1,4,13,42,...), A192800=(0,0,1,7,34,...).
MATHEMATICA
(See A192801.)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Jul 10 2011
EXTENSIONS
Recurrence corrected by Colin Barker, Jul 27 2012
STATUS
approved