A131436 -id:A131436 - cp's OEIS frontend

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

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

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

Original entry on oeis.org

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]

cp's OEIS Frontend

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

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

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

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cp's OEIS Frontend

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

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Maple

Formula

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

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Keywords

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Examples

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Formula

Extensions

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

Views

Author

Keywords

Comments

Examples

Crossrefs

Formula

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