A131439 -id:A131439 - cp's OEIS frontend

A131436 Triangle read by rows, (n-1) zeros followed by 2^n - 1.

1, 0, 3, 0, 0, 7, 0, 0, 0, 15, 0, 0, 0, 0, 31, 0, 0, 0, 0, 0, 63, 0, 0, 0, 0, 0, 0, 127, 0, 0, 0, 0, 0, 0, 0, 255, 0, 0, 0, 0, 0, 0, 0, 0, 511, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1023, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2047, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4095, 0, 0

Offset: 1

Gary W. Adamson, Jul 11 2007

			First few rows of the triangle are:
1;
0, 3;
0, 0, 7;
0, 0, 0, 15;
0, 0, 0, 0, 31;
...

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A131437, A131438, A131439.

Flatten[Table[{PadRight[{},n-1,0],2^n-1},{n,20}]] (* Harvey P. Dale, May 23 2012 *)

2*A059268(n)-A059268(n+1). - Paul Curtz, Jul 03 2008

More terms from Harvey P. Dale, May 23 2012

A131437 (A000012 * A131436) + (A131436 * A000012) - A000012.

Original entry on oeis.org

1, 3, 5, 7, 9, 13, 15, 17, 21, 29, 31, 33, 37, 45, 61, 63, 65, 69, 77, 93, 125, 127, 129, 133, 141, 157, 189, 253, 255, 257, 261, 269, 285, 317, 381, 509, 511, 513, 517, 525, 541, 573, 637, 765, 1021, 1023, 1025, 1029, 1037, 1053, 1085, 1149, 1277, 1533, 2045

Offset: 1

Gary W. Adamson, Jul 11 2007

Left column = 2^n - 1; right border = A036563, 2^(n+1) - 3: (1, 5, 13, 29, 61, 125, ...). Row sums = A131438: (1, 8, 29, 82, 207, 492, 1129, ...).

			First few rows of the triangle are:
1;
3, 5;
7, 9, 13;
15, 17, 21, 29;
31, 33, 37, 45, 61;
63, 65, 69, 77, 93, 125;
...

Cf. A036563, A131436, A131438, A131439.

A000012 := proc(n,k)
        1 ;
end proc:
A131436 := proc(n,k)
        if k = n then
                2^n-1 ;
        else
                0;
        end if;
end proc:
A131437 := proc(n,k)
        add( A000012(n,i)*A131436(i,k) + A131436(n,i)*A000012(i,k),i=k..n) -1 ;
end proc:
seq(seq(A131437(n,k),k=1..n),n=1..15) ; # R. J. Mathar, Sep 24 2011

(A000012 * A131436) + (A131436 * A000012) - A000012; as infinite lower triangular matrices.

Corrected by R. J. Mathar, Sep 24 2011

A131438 (2+n)2^n-2-3n.

Original entry on oeis.org

1, 8, 29, 82, 207, 492, 1129, 2534, 5603, 12256, 26589, 57306, 122839, 262100, 557009, 1179598, 2490315, 5242824, 11009989, 23068610, 48234431, 100663228, 209715129, 436207542, 905969587

Offset: 1

Gary W. Adamson, Jul 11 2007

Row sums of triangle A131437.

			a(3) = 19 = sum of row 3 terms of triangle A131437: (7 + 9 + 13).

Index entries for linear recurrences with constant coefficients, signature (6,-13,12,-4).

Cf. A131436, A131437, A131439.

Binomial transform of A131439.

G.f.: -x*(-1-2*x+6*x^2) / ( (2*x-1)^2*(x-1)^2 ). - R. J. Mathar, Sep 24 2011

Definition replaced by formula. - R. J. Mathar, Sep 24 2011

cp's OEIS Frontend

A131436 Triangle read by rows, (n-1) zeros followed by 2^n - 1.

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A131437 (A000012 * A131436) + (A131436 * A000012) - A000012.

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A131438 (2+n)2^n-2-3n.

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cp's OEIS Frontend

A131436 Triangle read by rows, (n-1) zeros followed by 2^n - 1.

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A131437 (A000012 * A131436) + (A131436 * A000012) - A000012.

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A131438 (2+n)*2^n-2-3*n.

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A131438 (2+n)2^n-2-3n.