On the $n$-arithmetical triangles constructed for polynomial coefficients
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2016), pp. 35-48.

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A fundamental solution system to a finite order linear difference equation with constant coefficients is considerably used during the investigation of the $n$-arithmetical triangles properties. The constructed fundamental solution system is explicitly expressed via the coefficients of the difference equation. The symmetric and unimodal properties of the polynomial coefficients sequence are proved and the formulas for these coefficient calculations are obtained.
Keywords: a linear difference equation
Mots-clés : polynomial coefficients.
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     title = {On the $n$-arithmetical triangles constructed for polynomial coefficients},
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V. E. Kruglov. On the $n$-arithmetical triangles constructed for polynomial coefficients. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2016), pp. 35-48. http://geodesic.mathdoc.fr/item/IVM_2016_8_a3/

[1] Bondarenko B. A., Obobschennye treugolniki i piramidy Paskalya, ikh fraktali, grafy i prilozheniya, Izd-vo “Fan”, Tashkent, 1990 | MR

[2] Tauber S., “Summation formulae for multinomial coefficients”, Fibonacci Quart., 3:2 (1965), 95–100 | MR | Zbl

[3] Abramson M., “Multinomial coefficients”, Math. Mag., 41:4 (1968), 199–205 | DOI | MR | Zbl

[4] Hoggatt V. E. (jr.), Alexanderson G. L., “A property of multinomial coefficients”, Fibonacci Quart., 9:4 (1971), 351–356 | MR | Zbl

[5] Hilliker D. H., “On the muitinomial theorem”, Fibonacci Quart., 15:1 (1977), 22–24 | MR | Zbl

[6] Shannon A. G., “A recurrence relation for generalized multinomial coefficients”, Fibonacci Quart., 17:4 (1979), 344–347 | MR | Zbl

[7] Gupta A. K., “On Pascal's triangle of the third kind”, Biometrische Z., 15 (1973), 389–392 | DOI | MR | Zbl

[8] Bollinger R. C., “A note on Pascal-$T$ triangles, multinomial coefficients, and Pascal pyramids”, Fibonacci Quart., 24:2 (1986), 140–144 | MR | Zbl

[9] Kruglov V. E., “Postroenie fundamentalnoi sistemy reshenii lineinogo raznostnogo uravneniya konechnogo poryadka”, Ukr. matem. zhurn., 61:6 (2009), 777–794 | MR | Zbl

[10] Kuzmin O. V., Obobschennye piramidy Paskalya i ikh prilozheniya, Sibirsk. izd-vo “Nauka”, Novosibirsk, 2000 | MR

[11] Aigner M., Kombinatornaya teoriya, Mir, M., 1982 | MR

[12] Shannon A. G., “Iterative formulas associated with generalized third order recurrence relations”, Siam J. Appl. Math., 23:3 (1972), 364–368 | DOI | MR | Zbl

[13] Pethe S., “Some identities for Tribonacci sequences”, Fibonacci Quart., 26:2 (1988), 144–151 | MR | Zbl

[14] Rabinowitz S., “Algorithmic manipulation of third-order linear recurrences”, Fibonacci Quart., 34:5 (1996), 447–464 | MR | Zbl

[15] Vilenkin V. Ya., Kombinatorika, Nauka, M., 1969 | MR