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A refined formula for the autocorrelation function of an M-sequence
Automation and Remote Control, 2015We consider a widespread impreciseness in the autocorrelation function formula for M-sequences. We propose a derivation of the exact expression for the normalized autocorrelation function for a p-ary sequence in almost all points of the temporal argument inside a period.
Boris F. Kir'yanov +2 more
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On a sequence of algebraic formulae of Ramanujan
The Mathematical Gazette, 2012Among the many astonishing formulae stated by Ramanujan we find in his Notebooks the following sequence (see [1], p 96, Entry 43): which hold for any triple of complex numbers ( a, b, c ) such that a + b + c = 0. Ramanujan concluded this list by ‘And so on’, which suggests that he had some kind of method or algorithm allowing him to extend ...
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On supplementary formulas for Sheffer sequences
Aequationes mathematicae, 2015The paper contains four theorems. In the first one, the author presents necessary and sufficient conditions for the Sheffer sequence to satisfy the supplementary formula. In the last three ones, characterizations of Bernoulli, Euler and poly-Bernoulli polynomials are given.
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Busy choice sequences refraining formulas and modalities
Studia Logica, 1995If one thinks of the operator `stit' in stit theory [see \textit{N. Belnap} and \textit{M. Perloff}, ``Seeing to it that: a canonical form for agentives'', in H. E. Kyburg jun., R. P. Loui and G. N. Carlson (eds.), Knowledge representation and defeasible reasoning, 169-190 (1990; Zbl 0743.68024)] as a modal operator, we may ask how many distinct ...
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Short resolution proofs for a sequence of tricky formulas
Acta Informatica, 1996zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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A Ramanujan Sequence that Refines the Cayley Formula for Trees
The Ramanujan Journal, 1999Using two entries of Ramanujan's second notebook a refinement of Cayley's formula for counting trees is proved, which generalizes a number of recent results in this direction.
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A formula for the generating functions of powers of Horadam's sequence [PDF]
Australas. J Comb., 2004 Let the sequence \(w_n=w_n(a,b;p,q)\) be given by the linear recurrence \(w_n=pw_{n-1}+ qw_{n-2}\) with \(w_0=a\) and \(w_1=b\). Horadam's sequence is then defined by \[ {\mathcal H}_k(x)={\mathcal H}_k (x;a,b;p,q)= \sum_{n\geq 0} w^k_nx^n. \] The main result of this paper is Theorem 1.1.
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A Formula for the Pell Sequence: 10663
The American Mathematical Monthly, 2000Emeric Deutsch +3 more
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The acquisition of formulaic sequences in EFL email writing
English for Specific Purposes, 2022Erik Fritz
exaly