0,5

Row sums of T form A000219 (planar partitions); row sums of T^2 form A000334(4-D); row sums of T^3 form A000416(6-D).

Matrix square of triangle A096651.

Triangle T begins:

{1},

{0,1},

{0,2,1},

{0,3,2,1},

{0,5,5,2,1},

{0,7,7,7,2,1},

{0,11,16,9,9,2,1},

{0,15,15,31,11,11,2,1},

{0,22,59,-4,54,13,13,2,1},

{0,30,-109,313,-72,87,15,15,2,1},

{0,42,1314,-1922,1122,-225,132,17,17,2,1},

{0,56,-11804,19468,-9671,3087,-509,191,19,19,2,1},

{0,77,133957,-217176,110734,-32581,7137,-980,266,21,21,2,1},

{0,101,-1728760,2809257,-1426436,422732,-87714,14601,-1704,359,23,23,2,1},...

Row sums are: {1,1,3,6,13,24,48,86,160,282,500,859,...} (A000219).

T^2 begins:

{1},

{0,1},

{0,4,1},

{0,10,4,1},

{0,26,14,4,1},

{0,59,38,18,4,1},

{0,140,109,50,22,4,1},

{0,307,256,179,62,26,4,1},

{0,684,709,370,273,74,30,4,1},

{0,1464,1240,1683,438,395,86,34,4,1},...

with row sums: {1,1,5,15,45,120,326,835,2145,5345,...} (A000334).

Cf. A096651, A000219, A000334, A000416.

Sequence in context: A025647 A025653 A131103 this_sequence A025654 A025648 A025655

Adjacent sequences: A096649 A096650 A096651 this_sequence A096653 A096654 A096655

sign,tabl

Paul D. Hanna (pauldhanna(AT)juno.com), Jul 06 2004