cp's OEIS Frontend

A374921 Irregular triangle read by rows: T(n,k), n >= 0, k >= 1, in which if n is even then row n lists the first A008619(n) even indexed terms of A027336 otherwise if n is odd then row n lists the first A008619(n) odd indexed terms of A027336.

%I A374921 #42 Nov 13 2024 17:26:00
%S A374921 1,1,1,1,1,2,1,1,3,1,2,4,1,1,3,6,1,2,4,8,1,1,3,6,11,1,2,4,8,15,1,1,3,
%T A374921 6,11,20,1,2,4,8,15,26,1,1,3,6,11,20,35,1,2,4,8,15,26,45,1,1,3,6,11,
%U A374921 20,35,58,1,2,4,8,15,26,45,75,1,1,3,6,11,20,35,58,96,1,2,4,8,15,26,45,75,121
%N A374921 Irregular triangle read by rows: T(n,k), n >= 0, k >= 1, in which if n is even then row n lists the first A008619(n) even indexed terms of A027336 otherwise if n is odd then row n lists the first A008619(n) odd indexed terms of A027336.
%C A374921 The sum of row n equals the number of partitions of n.
%e A374921 Triangle begins:
%e A374921   1;
%e A374921   1;
%e A374921   1, 1;
%e A374921   1, 2;
%e A374921   1, 1, 3;
%e A374921   1, 2, 4;
%e A374921   1, 1, 3, 6;
%e A374921   1, 2, 4, 8;
%e A374921   1, 1, 3, 6, 11;
%e A374921   1, 2, 4, 8, 15;
%e A374921   1, 1, 3, 6, 11, 20;
%e A374921   1, 2, 4, 8, 15, 26;
%e A374921   1, 1, 3, 6, 11, 20, 35;
%e A374921   1, 2, 4, 8, 15, 26, 45;
%e A374921   1, 1, 3, 6, 11, 20, 35, 58;
%e A374921   1, 2, 4, 8, 15, 26, 45, 75;
%e A374921   1, 1, 3, 6, 11, 20, 35, 58, 96;
%e A374921   1, 2, 4, 8, 15, 26, 45, 75, 121;
%e A374921   ...
%e A374921 For n = 10 the sum of the 10th row is 1 + 1 + 3 + 6 + 11 + 20 = 42, the same as the number of partitions of 10.
%Y A374921 Row sums give A000041.
%Y A374921 Row lengths give A008619.
%Y A374921 Right border gives A027336.
%Y A374921 Columns 1..4: A000012, A000034, A010702, A010724.
%Y A374921 Cf. A058695, A058696, A002865, A167430, A176206, A182844, A182845, A336811, A338156.
%K A374921 nonn,tabf
%O A374921 0,6
%A A374921 _Omar E. Pol_, Aug 01 2024