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A288842 Triangle (sans apex) of coefficients of terms of the form (eM_1)^j*(eM_2)^k re construction of triangle A287768. 0

%I #23 Jun 30 2019 04:41:25

%S 1,2,3,9,6,9,36,45,18,27,135,243,189,54,81,486,1134,1296,729,162,243,

%T 1701,4860,7290,6075,2673,486,729,5832,19683,36450,40095,26244,9477,

%U 1458,2187,19683,76545,168399,229635,199017,107163,32805,4374,6561,65610,288684,734832,1194102,1285956,918540,419904,111537,13122

%N Triangle (sans apex) of coefficients of terms of the form (eM_1)^j*(eM_2)^k re construction of triangle A287768.

%H G. G. Wojnar, D. Sz. Wojnar, and L. Q. Brin, <a href="http://arxiv.org/abs/1706.08381">Universal Peculiar Linear Mean Relationships in All Polynomials</a>, Table GW.n=3, p.22, arXiv:1706.08381 [math.GM], 2017.

%F T(n+1,k+1) = 3*T(n,k) + 3*T(n,k+1).

%e Triangle begins:

%e 1, 2;

%e 3, 9, 6;

%e 9, 36, 45, 18;

%t T[1, 1] = 1; T[1, 2] = 2;

%t T[n_, k_] /; 1 <= k <= n+1 := T[n, k] = 3 T[n-1, k-1] + 3 T[n-1, k];

%t T[_, _] = 0;

%t Table[T[n, k], {n, 1, 9}, {k, 1, n+1}] // Flatten (* _Jean-François Alcover_, Nov 16 2018 *)

%Y Columns are: A000244, A288834, A288835, A288836, A288838, etc.

%Y Cf. A287768.

%K nonn,tabf

%O 1,2

%A _Gregory Gerard Wojnar_, Jun 17 2017

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Last modified March 28 22:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)