A127752 -id:A127752 - cp's OEIS frontend

A127750 Row sums of inverse of number triangle A(n,k) = 1/(2n+1) if k <= n <= 2k, 0 otherwise.

1, 3, 2, 5, 2, 4, 2, 7, 2, 4, 2, 6, 2, 4, 2, 9, 2, 4, 2, 6, 2, 4, 2, 8, 2, 4, 2, 6, 2, 4, 2, 11, 2, 4, 2, 6, 2, 4, 2, 8, 2, 4, 2, 6, 2, 4, 2, 10, 2, 4, 2, 6, 2, 4, 2, 8, 2, 4, 2, 6, 2, 4, 2, 13, 2, 4, 2, 6, 2, 4, 2, 8, 2, 4, 2, 6, 2, 4, 2, 10, 2, 4, 2, 6, 2, 4, 2, 8, 2, 4, 2, 6, 2, 4, 2, 12, 2, 4, 2, 6, 2, 4, 2, 8, 2, 4

Offset: 0

Paul Barry, Jan 28 2007

nonn

Row sums of A127749.
Conjecture: a(n) mod 2 gives Fredholm-Rueppel sequence A036987.
The conjecture is true at least up to n=2048. - Antti Karttunen, Sep 29 2018

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

Cf. A127749, A127752.

A[n_, k_] := If[k <= n <= 2k, 1/(2n+1), 0];
Total /@ Inverse[Array[A, {128, 128}, {0, 0}]] (* Jean-François Alcover, Feb 10 2021 *)

up_to = 128;
A127750aux(n,k) = if(k<=n,if(n<=(2*k),1/(n+n+1),0),0);
A127750list(up_to) = { my(m1=matrix(up_to,up_to,n,k,A127750aux(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); };
v127750 = A127750list(1+up_to);
A127750(n) = v127750[1+n]; \\ Antti Karttunen, Sep 29 2018

More terms from Antti Karttunen, Sep 29 2018

A127751 Inverse of number triangle A(n,k)=if(k<=n,if(n<=2k,1/(3n+1),0),0).

Original entry on oeis.org

1, 0, 4, 0, -4, 7, 0, 4, -7, 10, 0, 0, 0, -10, 13, 0, -4, 7, 0, -13, 16, 0, 0, 0, 0, 0, -16, 19, 0, 4, -7, 10, 0, 0, -19, 22, 0, 0, 0, 0, 0, 0, 0, -22, 25, 0, 0, 0, -10, 13, 0, 0, 0, -25, 28, 0, 0, 0, 0, 0, 0, 0, 0, 0, -28, 31, 0, -4, 7, 0, -13

Offset: 0

Paul Barry, Jan 28 2007

Row sums A127752 mod 2 are conjectured to be first Feigenbaum symbolic sequence A035263.

			Triangle begins
  1;
  0,  4;
  0, -4,  7;
  0,  4, -7,  10;
  0,  0,  0, -10,  13;
  0, -4,  7,   0, -13,  16;
  0,  0,  0,   0,   0, -16,  19;
  0,  4, -7,  10,   0,   0, -19,  22;
  0,  0,  0,   0,   0,   0,   0, -22,  25;
  0,  0,  0, -10,  13,   0,   0,   0, -25,  28;
  0,  0,  0,   0,   0,   0,   0,   0,   0, -28,  31;
  0, -4,  7,   0, -13,  16,   0,   0,   0,   0, -31,  34;
  0,  0,  0,   0,   0,   0,   0,   0,   0,   0,   0, -34, 37;
Inverse of
  1;
  0, 1/4;
  0, 1/7, 1/7;
  0,  0,  1/10, 1/10;
  0,  0,  1/13, 1/13, 1/13;
  0,  0,   0,   1/16, 1/16, 1/16;
  0,  0,   0,   1/19, 1/19, 1/19, 1/19;
  0,  0,   0,    0,   1/22, 1/22, 1/22, 1/22;
  0,  0,   0,    0,   1/25, 1/25, 1/25, 1/25, 1/25;
  0,  0,   0,    0,    0,   1/28, 1/28, 1/28, 1/28, 1/28;
  0,  0,   0,    0,    0,   1/31, 1/31, 1/31, 1/31, 1/31, 1/31;

cp's OEIS Frontend

A127750 Row sums of inverse of number triangle A(n,k) = 1/(2n+1) if k <= n <= 2k, 0 otherwise.

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A127751 Inverse of number triangle A(n,k)=if(k<=n,if(n<=2k,1/(3n+1),0),0).

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