A131438 -id:A131438 - cp's OEIS frontend

A131439 Inverse binomial transform of A131438 (assuming zero offset in both sequences).

1, 7, 14, 18, 22, 26, 30, 34, 38, 42, 46, 50, 54, 58, 62, 66, 70, 74, 78, 82, 86, 90, 94, 98, 102, 106, 110, 114, 118, 122, 126, 130, 134, 138, 142, 146, 150, 154, 158, 162, 166, 170, 174, 178, 182

Offset: 1

Gary W. Adamson, Jul 11 2007

nonn

Conjecture: The sequence appears to be (1, 7, ...) followed by 4k + 14; k=0,1,2,...; thus: (1, 7, 14, 18, 22, 26, ...).

Inverse binomial transform of this sequence = (1, 6, 1, -4, 7, -10, 13, -16, 19, -22, ...).

			(1, 3, 3, 1) dot (1, 7, 14, 18) = 82 = A131438(4).

Cf. A131436, A131437, A131438.

A007318^(-1) * A131438.

a(n) = 2*a(n-1) - a(n-2) for n>4. G.f.: -x*(x+1)*(3*x^2-4*x-1) / (x-1)^2. [Colin Barker, Jan 06 2013]

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

Original entry on oeis.org

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

cp's OEIS Frontend

A131439 Inverse binomial transform of A131438 (assuming zero offset in both sequences).

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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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