

A134392


A077028 * A000012, that is Rascal's triangle (as matrix) multiplied by a lower triangular matrix of ones (main diagonal of ones included).


1



1, 2, 1, 4, 3, 1, 8, 7, 4, 1, 15, 14, 10, 5, 1, 26, 25, 20, 13, 6, 1, 42, 41, 35, 26, 16, 7, 1, 64, 63, 56, 45, 32, 19, 8, 1, 93, 92, 84, 71, 55, 38, 22, 9, 1, 130, 129, 120, 105, 86, 65, 44, 25, 10, 1, 176, 175, 165, 148, 126, 101, 75, 50, 28, 11, 1
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OFFSET

1,2


COMMENTS

Left border = A000125. Row sums = A134393: (1, 3, 8, 20, 45, 91, 168, 288,...).


LINKS

Table of n, a(n) for n=1..66.


FORMULA

A077028 * A000012 as infinite lower triangular matrices. Triangle read by rows, partial sums starting from the right of A077028.


EXAMPLE

First few rows of the triangle are;
1;
2, 1;
4, 3, 1;
8, 7, 4, 1;
15, 14, 10, 5, 1;
26, 25, 20, 13, 6, 1;
42, 41, 35, 26, 16, 7, 1;
...


MATHEMATICA

rows = 11;
R[n_, k_] /; k <= n := k (n  k) + 1; R[0, 0] = 1; R[_, _] = 0;
MR = Table[R[n, k], {n, 0, rows1}, {k, 0, rows1}];
MB = Table[Boole[0 <= k <= n], {n, 0, rows1}, {k, 0, rows 1}];
T = MR.MB;
Table[T[[n, k]], {n, 1, rows}, {k, 1, n}] // Flatten (* JeanFrançois Alcover, Apr 01 2020 *)


CROSSREFS

Cf. A077028, A000125, A134393.
Sequence in context: A134626 A115450 A109435 * A048483 A276562 A055248
Adjacent sequences: A134389 A134390 A134391 * A134393 A134394 A134395


KEYWORD

nonn,tabl


AUTHOR

Gary W. Adamson, Oct 23 2007


EXTENSIONS

Typos corrected by JeanFrançois Alcover, Apr 01 2020


STATUS

approved



