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Triangle, A004736 * A127899 (unsigned).
1

%I #12 Feb 18 2022 22:09:03

%S 1,4,2,7,7,3,10,12,10,4,13,17,17,13,5,16,22,24,22,16,6,19,27,31,31,27,

%T 19,7,22,32,38,40,38,32,22,8,25,37,45,49,49,45,37,25,9,28,42,52,58,60,

%U 58,52,42,28,10

%N Triangle, A004736 * A127899 (unsigned).

%C Row sums = A084990: (1, 6, 17, 36, 65, 106, ...).

%C A128225 = A127899(unsigned) * A004736.

%F A004736 * A127899 (unsigned). By columns, (3k+1), (5k+2), (7k+3), ...; k=0,1,2...

%e First few row of the triangle are:

%e 1;

%e 4, 2;

%e 7, 7, 3;

%e 10, 12, 10, 4;

%e 13, 17, 17, 13, 5;

%e 16, 22, 24, 22, 16, 6;

%e 19, 27, 31, 31, 27, 19, 7;

%e ...

%t (* a127899U computes the unsigned version of A127899 *)

%t a127899U[n_, k_] := If[n==k||n-1==k, n, 0]/;(1<=k<=n)

%t a004736[n_, k_] := n-k+1/;(1<=k<=n+1)

%t a128225[n_, k_] := a127899U[n, n](a004736[n, k] + a004736[n-1, k])/;(1<=k<=n)

%t a128225[r_] := Table[a128225[n, k], {n, 1, r}, {k, 1, n}]

%t TableForm[a128225[7]] (* triangle *)

%t Flatten[a128225[10]] (* data *) (* _Hartmut F. W. Hoft_, Mar 13 2017 *)

%Y Cf. A004736, A084990, A127899, A128225.

%K nonn,tabl

%O 1,2

%A _Gary W. Adamson_, Feb 19 2007