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A046854^2 as an infinite lower triangular matrix.
3

%I #12 Feb 28 2022 12:09:58

%S 1,2,1,3,2,1,5,5,2,1,8,9,7,2,1,13,19,13,9,2,1,21,33,34,17,11,2,1,34,

%T 65,61,53,21,13,2,1,55,111,141,97,76,25,15,2,1,89,210,248,257,141,103,

%U 29,17,2,1,144,355,534,461,421,193,134,33,19,2,1

%N A046854^2 as an infinite lower triangular matrix.

%C Left border = Fibonacci numbers.

%C Row sums = A131246.

%C A131243 is the square of the reflection triangle to A046854: A065941.

%C Row sums of A131243 = (1, 3, 6, 14, 30, 67, 146, 322, 705, 1549, ...).

%e First few rows of the triangle:

%e 1;

%e 2, 1;

%e 3, 2, 1;

%e 5, 5, 2, 1;

%e 8, 9, 7, 2, 1;

%e 13, 19, 13, 9, 2, 1;

%e 21, 33, 34, 17, 11, 2, 1;

%e ...

%o (PARI) T(n, k) = binomial((n+k)\2, k);

%o row(n) = my(m=matrix(n+1, n+1, i, j, T(i-1,j-1))); vector(n+1, i, (m^2)[n+1,i]);

%o lista(nn) = for (n=0, nn, my(v=row(n)); for (i=1, #v, print1(v[i], ", "));); \\ _Michel Marcus_, Feb 28 2022

%Y Cf. A131243, A131244, A131246, A046854, A065941.

%K nonn,tabl

%O 0,2

%A _Gary W. Adamson_, Jun 22 2007

%E More terms from _Michel Marcus_, Feb 28 2022