

A096227


Number of different triangles created when a square sheet of paper is folded n times, the first time by one of the diagonal of the square sheet and the by the median of the square triangle.


3



2, 8, 16, 44, 96, 268, 648, 1832, 4784, 13456, 36832, 102944, 289216, 804928, 2292608, 6365312, 18257664, 50626816, 145731072, 403833344
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OFFSET

1,1


LINKS

Table of n, a(n) for n=1..20.
Index entries for linear recurrences with constant coefficients, signature (0,14,0,56,0,64).


FORMULA

a(1)=2, a(2)=8, a(3)=16, a(4)=44, a(5)=96 are easily counted. Now if n even > 4 define X(4)=10 and X(n)=2*(X(n2)1), then a(n)=3*2^(3*(n/2)1) + 2^((n/2)1)*(2*X(n2)1); if n odd > 5 define X(5)=8 and Y(5)=2, X(n)=4*X(n2)5*(2*Y(n2)1) and Y(n)=2*Y(n2)1 then a(n)=2^(3*(((n+1)/2)1)) + 2^(((n+1)/2)1)*(4*X(n2)5*(2*(Y(n2)1)
For n>3, satisfies a linear recurrence with characteristic polynomial (12x)(1+2x)(12x^2)(18x^2).
G.f.: 2*x*(32*x^8+16*x^7+36*x^6+50*x^58*x^434*x^36*x^2+4*x+1)/((2*x1)*(2*x+1)*(2*x^21)*(8*x^21)). [Colin Barker, Oct 21 2012]


EXAMPLE

For n odd X(5)=8 Y(5)=2
X(7)=17 Y(7)=3
X(9)=43 Y(9)=5
X(11)=127 Y(11)=9


CROSSREFS

Sequence in context: A232392 A176143 A296946 * A191309 A323351 A134353
Adjacent sequences: A096224 A096225 A096226 * A096228 A096229 A096230


KEYWORD

nonn,easy


AUTHOR

Pierre CAMI, Aug 11 2004


STATUS

approved



