A127752 Row sums of inverse of number triangle A(n,k) = 1/(3n+1) if k <= n <= 2k, 0 otherwise.

1, 4, 3, 7, 3, 6, 3, 10, 3, 6, 3, 9, 3, 6, 3, 13, 3, 6, 3, 9, 3, 6, 3, 12, 3, 6, 3, 9, 3, 6, 3, 16, 3, 6, 3, 9, 3, 6, 3, 12, 3, 6, 3, 9, 3, 6, 3, 15, 3, 6, 3, 9, 3, 6, 3, 12, 3, 6, 3, 9, 3, 6, 3, 19, 3, 6, 3, 9, 3, 6, 3, 12, 3, 6, 3, 9, 3, 6, 3, 15, 3, 6, 3, 9, 3, 6, 3, 12, 3, 6, 3, 9, 3, 6, 3, 18, 3, 6, 3, 9, 3, 6, 3, 12, 3, 6

Offset

0,2

Comments

Row sums of number triangle A127751.

a(n) mod 2 is first Feigenbaum symbolic sequence A035263 (conjecture).

The conjecture is true at least up to 2048 first terms. (But please note the different indexing, here 0-based.) - Antti Karttunen, Sep 29 2018

Links

Antti Karttunen, Table of n, a(n) for n = 0..2048

Mathematica

A[n_, k_] := If[k <= n <= 2k, 1/(3n+1), 0];
Total /@ Inverse[Array[A, {128, 128}, {0, 0}]] (* Jean-François Alcover, Feb 11 2021 *)

Prog

(PARI)
up_to = 128;
A127752aux(n, k) = if(k<=n, if(n<=(2*k), 1/((3*n)+1), 0), 0);
A127752list(up_to) = { my(m1=matrix(up_to, up_to, n, k, A127752aux(n-1, k-1)), m2 = matsolve(m1, matid(up_to)), v = vector(up_to)); for(n=1, up_to, v[n] = vecsum(m2[n, ])); (v); };
v127752 = A127752list(1+up_to);
A127752(n) = v127752[1+n]; \\ Antti Karttunen, Sep 29 2018

Crossrefs

Cf. A127750, A127751.

Sequence in context: A072816 A340012 A046548 * A198874 A276760 A365214

Adjacent sequences: A127749 A127750 A127751 * A127753 A127754 A127755

Keyword

nonn

Author

Paul Barry, Jan 28 2007

Extensions

More terms from Antti Karttunen, Sep 29 2018

Status

approved