|
| |
|
|
A116466
|
|
Unsigned row sums of triangle A114700.
|
|
2
| |
|
|
1, 2, 2, 4, 2, 4, 4, 8, 10, 20, 32, 64, 112, 224, 408, 816, 1514, 3028, 5680, 11360, 21472, 42944, 81644, 163288, 311896, 623792, 1196132, 2392264, 4602236, 9204472, 17757184, 35514368, 68680170, 137360340, 266200112, 532400224, 1033703056
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,2
|
|
|
COMMENTS
| Both triangles A112555 and A114700 have the property that the m-th matrix power of the triangles satisfy T^m = I + m*(T - I). So it is curious that the row squared sums of A112555 is a bisection of the unsigned row sums of A114700.
|
|
|
FORMULA
| G.f.: (1+2*x)*( 2*(1+x^2)/(1-x^2) + x^2/(1-4*x^2)^(1/2) )/(2+x^2). Also, a(2*n+1) = 2*a(2*n), a(2*n) = A112556(n), where A112556 equals the row squared sums of triangle A112555.
|
|
|
PROG
| (PARI) {a(n)=local(x=X+X*O(X^n)); polcoeff((1+2*x)*(2*(1+x^2)/(1-x^2)+x^2/(1-4*x^2)^(1/2))/(2+x^2), n, X)} (PARI) /* a(n) as the unsigned row sums of A114700 */ {a(n)=sum(k=0, n, abs(polcoeff(polcoeff(1/(1-x*y)+ x*(1+x-2*x^2*y)/(1-x)/(1+x+x*y+x*O(x^n)+y*O(y^k))/(1-x*y), n, x), k, y)))}
|
|
|
CROSSREFS
| Cf. A112556, A112555, A114700.
Sequence in context: A001316 A161831 A096865 * A116467 A079314 A060609
Adjacent sequences: A116463 A116464 A116465 * A116467 A116468 A116469
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Feb 19 2006
|
| |
|
|
