A055877 Least increasing sequence with a(1) = 1 and Hankel transform {1,1,1,1,...}.

1, 2, 5, 6, 42, 43, 18626, 18627, 5798368522871, 5798368522872, 194935493755610196550803104551677768964, 194935493755610196550803104551677768965

Offset

1,2

Comments

Hankel transform {t(n)} of {a(n)} is given by t(n) = Det[{a(1), a(2), ..., a(n)}, {a(2), a(3), ..., a(n+1)}, ..., {a(n), a(n+1), ..., a(2n-1)}].

Links

Thomas Scheuerle, Table of n, a(n) for n = 1..18

Example

Given that {a(n)} = {1,2,5,6,a(5),...}, a(5) is seen to be 42 since Det[{1,2,5},{2,5,6},{5,6,42}] = 1, whereas Det[{1,2,5},{2,5,6},{5,6,43}] = 2.

Prog

(PARI)
\\ The functions solve1 and HankelZi contain code copied from Michael Somos
{solve1(ex, v=0) = my(ex0, ex1); if(v, , v=variable(ex)); ex0=polcoeff(ex, 0, v); ex1=polcoeff(ex, 1, v); if(ex1 && (ex==v*ex1+ex0), -ex0/ex1, 'UNDEF)};
{HankelZi(vb, va) = my(an, ln); va[1]=vb[1]; va[2]=vb[2]; ln = #va+1; va=concat(va, [0, 0]); for(n=ln, #vb, va[n]='x; an=solve1(matdet(matrix((n+1)\2, (n+1)\2, i, j, va[i+j-1+(n+1)%2]))-vb[n]); va[n]=an); va};
{nextvalue(vb, va) = my(va=HankelZi(concat(vb, [1, 'y]), va), vr=Vec((va[#va]-1))); vb=concat(vb, [1, vr[2]/-vr[1]]); va[#va]=va[#va-1]+1; [vb, va]};
listA(max_n) = my(r=[[1, 2], [1, 2]]); for(n=2, ceil(max_n/2), r=nextvalue(r[1], r[2])); r[2] \\ Thomas Scheuerle, Jan 07 2026

Crossrefs

Cf. A055879, A350349, A376277.

Sequence in context: A152918 A276845 A365503 * A288799 A281378 A219117

Adjacent sequences: A055874 A055875 A055876 * A055878 A055879 A055880

Keyword

nonn

Author

John W. Layman, Jul 14 2000

Status

approved