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A308663
Partial sums of A097805.
0
1, 1, 2, 2, 3, 4, 4, 5, 7, 8, 8, 9, 12, 15, 16, 16, 17, 21, 27, 31, 32, 32, 33, 38, 48, 58, 63, 64, 64, 65, 71, 86, 106, 121, 127, 128, 128, 129, 136, 157, 192, 227, 248, 255, 256, 256, 257, 265, 293, 349, 419, 475, 503, 511, 512
OFFSET
0,3
COMMENTS
Curtz (1965), page 15, from right to left, gives (F1):
1/2;
1/4, 3/4;
1/8, 4/8, 7/8;
1/16, 5/16, 11/16, 15/16;
... .
Numerators + Denominators = (C) =
3;
5, 7;
9, 12, 15;
17, 21, 27, 31;
... .
This is the current sequence without powers of 2.
The triangle (P) for a(n) is
1;
1, 2;
2, 3, 4;
4, 5, 7, 8;
8, 9, 12, 15, 16;
... .
(C) is the core of (P).
Extension of (F1). (F2) =
0/1;
0/1, 1/1;
0/2, 1/2, 2/2;
0/4, 1/4, 3/4, 4/4;
0/8, 1/8, 4/8, 7/8, 8/8;
... .
(Mentioned, without 0's, op. cit., page 16.)
a(n) = Numerators + Denominators.
Row sums of triangle (P): A084858(n).
From right to left, with alternating signs: 1, 1, 3, 2, 12, 8, 48, 32, ..., see A098646.
For triangle (C), row sums give A167667(n+1).
From right to left, with alternating signs: A098646(n).
Rank of A016116(n): 0 together with A117142.
LINKS
Paul Curtz, Accélération de la convergence de certaines séries alternées à l'aide des fonctions de sommation, Thèse de 3ème Cycle d'Analyse Numérique, Faculté des Sciences de l'Université de Paris, 4 mai 1965.
FORMULA
T(n,k) = ceiling(2^(n-1)) + Sum_{j=0..k-1} binomial(n-1,j). - Alois P. Heinz, Jun 15 2019
a(n+1) = a(n) + A097805(n+1) for n >= 0.
CROSSREFS
Cf. A097805.
Sequence in context: A153155 A225085 A134310 * A305713 A259201 A342518
KEYWORD
nonn,tabl
AUTHOR
Paul Curtz, Jun 15 2019
EXTENSIONS
Edited by N. J. A. Sloane, Sep 15 2019
STATUS
approved