cp's OEIS Frontend

A096653 Lower triangular matrix T, read by rows, such that the row sums of T^n form the (3n)-dimensional partition numbers.

%I A096653 #3 Mar 30 2012 18:36:40
%S A096653 1,0,1,0,3,1,0,6,3,1,0,13,9,3,1,0,24,19,12,3,1,0,48,48,25,15,3,1,0,86,
%T A096653 84,84,31,18,3,1,0,160,228,99,135,37,21,3,1,0,282,129,721,57,204,43,
%U A096653 24,3,1,0,500,2521,-2267,2087,-93,294,49,27,3,1,0,859,-16291,29876,-13253,5229,-417,408,55,30,3,1,0,1479,199621,-317919
%N A096653 Lower triangular matrix T, read by rows, such that the row sums of T^n form the (3n)-dimensional partition numbers.
%C A096653 Row sums of T form A000293 (solid partitions); row sums of T^2 form A000416(6-D).
%F A096653 Matrix cube of triangle A096651.
%e A096653 Triangle T begins:
%e A096653 {1},
%e A096653 {0,1},
%e A096653 {0,3,1},
%e A096653 {0,6,3,1},
%e A096653 {0,13,9,3,1},
%e A096653 {0,24,19,12,3,1},
%e A096653 {0,48,48,25,15,3,1},
%e A096653 {0,86,84,84,31,18,3,1},
%e A096653 {0,160,228,99,135,37,21,3,1},
%e A096653 {0,282,129,721,57,204,43,24,3,1},
%e A096653 {0,500,2521,-2267,2087,-93,294,49,27,3,1},
%e A096653 {0,859,-16291,29876,-13253,5229,-417,408,55,30,3,1},
%e A096653 {0,1479,199621,-317919,165456,-46401,11539,-996,549,61,33,3,1},
%e A096653 {0,2485,-2547804,4150781,-2100853,627628,-126896,23006,-1926,720,67,36,3,1},...
%e A096653 Row sums are: {1,1,4,10,26,59,140,307,684,1464,3122,6500,...} (A000293).
%e A096653 T^2 begins:
%e A096653 {1},
%e A096653 {0,1},
%e A096653 {0,6,1},
%e A096653 {0,21,6,1},
%e A096653 {0,71,27,6,1},
%e A096653 {0,216,101,33,6,1},
%e A096653 {0,657,363,131,39,6,1},
%e A096653 {0,1907,1185,552,161,45,6,1},
%e A096653 {0,5507,3931,1824,789,191,51,6,1},
%e A096653 {0,15522,11574,7449,2520,1080,221,57,6,1},...
%e A096653 with row sums: {1,1,7,28,105,357,1197,3857,12300,38430,...} (A000416).
%Y A096653 Cf. A096651, A096652, A000293, A000416.
%K A096653 sign,tabl
%O A096653 0,5
%A A096653 _Paul D. Hanna_, Jul 06 2004