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 A177993 Triangle read by rows, A177990 * A007318. 4

%I #12 Apr 14 2021 05:23:44

%S 1,1,1,2,3,1,2,4,3,1,3,8,9,5,1,3,9,13,11,5,1,4,15,28,31,20,7,1,4,16,

%T 34,46,40,22,7,1,5,24,62,102,110,78,35,9,1,5,25,70,130,166,148,91,37,

%U 9,1,6,35,115,250,376,400,301,157,54,11,1,6,36,125,295,496,610,553,367,174,56,11,1

%N Triangle read by rows, A177990 * A007318.

%H Andrew Howroyd, <a href="/A177993/b177993.txt">Table of n, a(n) for n = 0..1325</a> (rows 0..50)

%F As infinite lower triangular matrices, A177990 * Pascal's triangle, (A007318).

%F T(n,k) = binomial(n,k) + Sum_{j=0..floor(n/2)-1} binomial(2*j+1,k). - _Andrew Howroyd_, Apr 13 2021

%e First few rows of the triangle =

%e 1;

%e 1, 1;

%e 2, 3, 1;

%e 2, 4, 3, 1;

%e 3, 8, 9, 5, 1;

%e 3, 9, 13, 11, 5, 1;

%e 4, 15, 28, 31, 20, 7, 1;

%e 4, 16, 34, 46, 40, 22, 7, 1;

%e 5, 24, 62, 102, 110, 78, 35, 9, 1;

%e 5, 25, 70, 130, 166, 148, 91, 37, 9, 1;

%e 6, 35, 115, 250, 376, 400, 301, 157, 54, 11, 1;

%e 6, 36, 125, 295, 496, 610, 553, 367, 174, 56, 11, 1;

%e 7, 48, 191, 515, 991, 1402, 1477, 1159, 669, 276, 77, 13, 1;

%e 7, 49, 203, 581, 1211, 1897, 2269, 2083, 1461, 771, 297, 709, 13, 1;

%e ...

%o (PARI) T(n,k) = {binomial(n,k) + sum(j=0, n\2-1, binomial(2*j+1,k))} \\ _Andrew Howroyd_, Apr 13 2021

%Y Row sums are A061547(n+1).

%Y Cf. A177992 = A007318 * A177990.

%Y Cf. A061547.

%K nonn,tabl

%O 0,4

%A _Gary W. Adamson_, May 16 2010

%E Terms a(55) and beyond from _Andrew Howroyd_, Apr 13 2021

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Last modified February 21 14:42 EST 2024. Contains 370236 sequences. (Running on oeis4.)