A151755 -id:A151755 - cp's OEIS frontend

A151756 The rows of (A151755 written as a triangle) converge to this sequence.

0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 0, 1, 5, 6, 0, 0, 0, 0, 0, 1, 4, 4, 0, 0, 0, 0, 1, 7, 17, 14, 0, 0, 0, 0, 0, 1, 4, 4, 0, 0, 0, 0, 1, 7, 16, 12, 0, 0, 0, 0, 1, 6, 12, 8, 0, 0, 0, 1, 9, 31, 49, 30, 0, 0, 0, 0, 0, 1, 4, 4, 0, 0, 0, 0, 1, 7, 16, 12, 0, 0, 0, 0, 1, 6, 12, 8, 0, 0, 0, 1, 9, 31, 48, 28, 0, 0

Offset: 0

N. J. A. Sloane, Jun 21 2009

nonn

Cf. A151755.

A151795 Let P = g.f. for A151755, then g.f. for present sequence is G = (P-(x^7+x^15+x^31+x^63+...))/(1+2*x).

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 3, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 3, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 0, 1, 5, 7, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 3, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 0, 1, 5, 7, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0

Offset: 0

N. J. A. Sloane, Jun 26 2009

nonn

This was an attempt (so far unsuccessful) to find a closed form for P.

			G = x^14 + x^22 + x^29 + 3*x^30 + x^38 + x^45 + 3*x^46 + x^53 + 2*x^54 + x^60 + 5*x^61 + 7*x^62 + x^70 + x^77 + 3*x^78 + x^85 + 2*x^86 + x^92 + 5*x^93 + 7*x^94 + x^101 + 2*x^102 + x^108 + 5*x^109 + 6*x^110 + x^116 + 4*x^117 + 4*x^118 + x^123 + 7*x^124 + 17*x^125 + 15*x^126 + ...

Cf. A151755.

A151757 Positive integers n, excluding 1 and 2^i+1 for all i, having wt <= 3.

Original entry on oeis.org

4, 6, 7, 8, 10, 11, 12, 13, 14, 16, 18, 19, 20, 21, 22, 24, 25, 26, 28, 32, 34, 35, 36, 37, 38, 40, 41, 42, 44, 48, 49, 50, 52, 56, 64, 66, 67, 68, 69, 70, 72, 73, 74, 76, 80, 81, 82, 84, 88, 96, 97, 98, 100, 104, 112, 128, 130, 131, 132, 133, 134, 136, 137, 138, 140, 144, 145, 146

Offset: 1

N. J. A. Sloane, Jun 21 2009

nonn

Arises in analyzing A151755.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A000120, A048645, A151755.

N:= 8: # for terms <= 2^(N+1)
Res1:= {seq(2^i,i=2..N)}:
Res2:= {seq(seq(2^i+2^j,i=1..j-1),j=2..N)}:
Res3:= {seq(seq(seq(2^i+2^j+2^k, i=0..j-1),j=1..k-1),k=2..N)}:
sort(convert(Res1 union Res2 union Res3,list)); # Robert Israel, Mar 27 2020

cp's OEIS Frontend

A151756 The rows of (A151755 written as a triangle) converge to this sequence.

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A151795 Let P = g.f. for A151755, then g.f. for present sequence is G = (P-(x^7+x^15+x^31+x^63+...))/(1+2*x).

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A151757 Positive integers n, excluding 1 and 2^i+1 for all i, having wt <= 3.

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