A106399 Binomial transform of A100060.

1, 1, 2, 4, 8, 16, 31, 58, 107, 200, 387, 782, 1640, 3512, 7542, 16020, 33406, 68257, 136971, 271341, 534302, 1053441, 2092840, 4206655, 8564397, 17631551, 36575711, 76137143, 158427407, 328537434, 677598776, 1388303692, 2824261172, 5704560206, 11443336382

Offset

1,3

Comments

1 or 0 are assigned to increase or decrease in magnitude of a succession of terms in the first difference row of Zeta function heights, as recorded in A100060.

Links

Table of n, a(n) for n=1..35.

Formula

Use the binomial transform operation (bto) on A100060, i.e. (bto): [1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1,

Example

a(5) = 8 = 1*1 + 4*0 + 6*1 + 4*0 + 1*1.

Mathematica

nmax = 40; A100060 = (Sign[Differences[Im[ZetaZero[Range[nmax+2]]], 2]] + 1)/2; Flatten[{1, Table[1 + Sum[Binomial[n, k]*A100060[[k]], {k, 1, n}], {n, 1, nmax}]}] (* Vaclav Kotesovec, Nov 28 2017 *)

Crossrefs

Cf. A100060.

Sequence in context: A133552 A174439 A000128 * A334636 A299026 A007800

Adjacent sequences: A106396 A106397 A106398 * A106400 A106401 A106402

Keyword

nonn

Author

Gary W. Adamson, May 01 2005

Extensions

a(11) corrected by Vaclav Kotesovec, Nov 28 2017

More terms from Vaclav Kotesovec, Nov 28 2017

Status

approved