A116466 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

A116466

Unsigned row sums of triangle A114700.

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; text; 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.

LINKS

Table of n, a(n) for n=0..36.

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.

MATHEMATICA

CoefficientList[Series[(1 + 2*x)*(2*(1 + x^2)/(1 - x^2) + x^2/(1 - 4*x^2)^(1/2))/(2 + x^2), {x, 0, 50}], x] (* Wesley Ivan Hurt, Feb 21 2017 *)

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: A364567 A161831 A096865 * A116467 A079314 A323381

Adjacent sequences: A116463 A116464 A116465 * A116467 A116468 A116469

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Feb 19 2006

STATUS

approved