A134389 A transform of floor((n+2)/2) with Hankel transform floor((n+2)/2)*(cos(Pi*n/2) + sin(Pi*n/2)).

1, 2, 5, 11, 24, 51, 108, 226, 472, 979, 2028, 4182, 8616, 17694, 36312, 74340, 152112, 310659, 634188, 1292686, 2633992, 5360362, 10905480, 22163676, 45032784, 91417646, 185539448, 376279196

Offset

0,2

Comments

Transform of floor((n+2)/2) = 1,1,2,2,3,3,4,4,... (A008619) under the array A134388. Hankel transform is the signed version of A008619 given by 1,1,-2,-2,3,3,-4,4,....

Links

Table of n, a(n) for n=0..27.

Formula

G.f.: ((2-x)/(1-2*x) + x*sqrt(1-4*x^2)/(1-2*x)^2)/2.

Conjecture: (n-1)*a(n) - 2*n*a(n-1) + 4*(4-n)*a(n-2) + 8*(n-3)*a(n-3) = 0. - R. J. Mathar, Oct 25 2012

a(n) ~ 2^(n - 1/2) * sqrt(n/Pi) * (1 + 3*sqrt(2*Pi/n)/4). - Vaclav Kotesovec, Apr 11 2021

Crossrefs

Cf. A008619, A134388.

Sequence in context: A182557 A027934 A336482 * A286945 A371797 A350326

Adjacent sequences: A134386 A134387 A134388 * A134390 A134391 A134392

Keyword

easy,nonn

Author

Paul Barry, Oct 23 2007

Status

approved