A163946 - OEIS

%I #16 Jan 22 2023 09:15:55

%S 1,1,1,2,2,2,5,5,6,6,14,14,18,24,22,42,42,56,84,110,92,132,132,180,

%T 288,440,552,426,429,429,594,990,1650,2484,2982,2150,1430,1430,2002,

%U 3432,6050,10120,14910,17200,11708,4862,4862,6864,12012,22022,39468,65604,94600,105372,68282

%N Triangle read by rows, A033184 * A091768 (diagonalized as an infinite lower triangular matrix).

%C As an eigentriangle, equals A033184 * the diagonalized version of its eigensequence. (the eigensequence of triangle A033184 = A091768).

%C Right border = A091768, left border = Catalan sequence A000108.

%C Sum of n-th row terms = rightmost term of next row.

%F Triangle read by rows, A033184 * A091768 (diagonalized such that the right border = (1, 1, 2, 6, 22, 92, 426, 2150,...) i.e. A091768 prefaced with a 1; with the rest zeros).

%e First few rows of the triangle =

%e   1;

%e   1, 1;

%e   2, 2, 2;

%e   5, 5, 6, 6;

%e   14, 14, 18, 24, 22;

%e   42, 42, 56, 84, 110, 92;

%e   132, 132, 180, 288, 440, 552, 426;

%e   429, 429, 594, 990, 1650, 2484, 2982, 2150;

%e   1430, 1430, 2002, 3432, 6050, 10120, 14910, 17200, 11708;

%e   4862, 4862, 6864, 12012, 22022, 39468, 65604, 94600, 105372, 68282;

%e   ...

%e Row 3 = (5, 5, 6, 6) = (5, 5, 3, 1) * (1, 1, 2, 6); where (5, 5, 3, 1) = row 3 of triangle A033184 and (1, 1, 2, 6) = the first 3 terms of A091768 prefaced with a 1.

%Y Cf. A033184, A091768, A000108, A071721.

%K nonn,tabl

%O 0,4

%A _Gary W. Adamson_, Aug 06 2009