19 problems

Let $r(x)$ be the generating function of the Rueppel sequence, and let the Hankel transform be reduced termwise modulo $2$. Modulo-2 periodicity conjecture. The Hankel transform of…

Let $r(x)$ be the generating function of the Rueppel sequence, and let the Hankel transform of a sequence be the sequence of determinants of its successive Hankel matrices. Periodi…

Let $r(x)$ be the generating function of the Rueppel sequence, and let the Hankel transform be the sequence of determinants of successive Hankel matrices. A005811 Hankel-transform…

Let $r(x)$ be the generating function of the Rueppel sequence, and let the Hankel transform be the sequence of determinants of successive Hankel matrices. A005811 Hankel-transform…

Let $r_n$ be the Rueppel sequence. Let $H_n$ be the Hankel transform of the sequence $1-r_n$, and let $h_n$ be the Hankel transform of the first-difference sequence $r_{n+1}-r_n$.…

Let $h_n$ be the Hankel transform of the Rueppel sequence $r_n$, and let $H_n$ be the Hankel transform of the once-shifted Rueppel sequence $r_{n+1}$. A268411 product conjecture. T…

General Hankel-transform conjecture. The Hankel transform is given by

Let $a_n(p,s,t)$ be the generalized Schröder numbers and let $h_n(p,s,t)$ be their Hankel transform. A $(\alpha,\beta)$ Somos $4$ sequence satisfies … Generalized Schröder Somos 4…

Let $E=E(a,b,c,d)$ be the elliptic curve … with nonzero discriminant, and let $(0,0)$ be the reference point. Let $h_n$ be the Hankel transform of the sequence generated by … where…

Robbins-number conjecture. The Hankel transform of this revert transform is the Robbins number sequence

Structured discrete Hankel-transform conjecture. The following pairs are feasible:

Discrete Hankel-transform feasibility conjecture. If $(k,q)$ is $(s,\nu)$-feasible, then $(k+1,q)$ and $(k,q-1)$ are $(s,\nu)$-feasible. The function…

Somos 4 conjecture. The Hankel transform of the expansion of $f(x)/x$ is a

Let $t$ be a parameter and let $a_n$ be the sequence whose generating function is … Transformed elliptic-curve Somos 4 conjecture. The Hankel transform of $a_n$ is a $(1,t^2+3t+1)$…

Let $b_n$ be the sequence whose generating function is … arising from the elliptic-curve family $E_t:y^2+4xy+y=x^3+(t-1)x^2+tx$. A $(\alpha,\beta)$ Somos $4$ sequence satisfies … E…

Let $c(x)$ denote the Catalan generating function and define a sequence by … Define … … Cubic-family Hankel-transform conjecture. The Hankel transform of the sequence with generati…

Let $a_n(\beta)$ be defined by … with $a_0=1$, $a_1=0$, and $a_2=\beta$, and let $h_n(\beta)$ be its Hankel transform. Recurrence-form Hankel-transform conjecture. The Hankel trans…

Let $a_n(p,q,r,s,t)$ be the five-parameter generalized Catalan sequence. Assume … Specialized generalized Catalan Somos 4 conjecture. The Hankel transform of $a_n(p,q,1,q-p+1,1)$ i…

Let $a_n(p,q,r,s,t)$ be the five-parameter generalized Catalan sequence and let $h_n$ denote the Hankel transform of $\frac{1}{p}a_{n+1}(p,q,r,s,t)$. A $(\alpha,\beta)$ Somos $4$ s…