A274637 -id:A274637 - cp's OEIS frontend

A274638 Main diagonal of A274637.

0, 0, 3, 5, 15, 27, 63, 119, 255, 495, 1023, 2015, 4095, 8127, 16383, 32639, 65535, 130815, 262143, 523775, 1048575, 2096127, 4194303, 8386559, 16777215, 33550335, 67108863, 134209535, 268435455, 536854527, 1073741823, 2147450879, 4294967295, 8589869055, 17179869183, 34359607295, 68719476735

Offset: 0

N. J. A. Sloane, Jul 08 2016

Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,0,-6,4).

Cf. A274637.

LinearRecurrence[{3, 0, -6, 4}, {0, 0, 3, 5}, 50] (* Paolo Xausa, Oct 21 2024 *)

concat([0,0], Vec(x^2*(3-4*x)/((1-x)*(1-2*x)*(1-2*x^2)) + O(x^40))) \\ Colin Barker, Jul 09 2016

From Colin Barker, Jul 09 2016: (Start)
a(n) = (-1+2^n+2^((n-3)/2)*(-1+(-1)^n)).
a(n) = 2^n-1 for n even.
a(n) = 2^n-1-2^((n-1)/2) for n odd.
a(n) = 3*a(n-1)-6*a(n-3)+4*a(n-4) for n>3.
G.f.: x^2*(3-4*x) / ((1-x)*(1-2*x)*(1-2*x^2)).
(End)

A274636 Square array read by antidiagonals: T(m,n) (m>=0, n>=0) = (2^floor(m/2)+1)*(2^ceiling(n/2)+1).

Original entry on oeis.org

4, 4, 6, 6, 6, 6, 6, 9, 6, 10, 10, 9, 9, 10, 10, 10, 15, 9, 15, 10, 18, 18, 15, 15, 15, 15, 18, 18, 18, 27, 15, 25, 15, 27, 18, 34, 34, 27, 27, 25, 25, 27, 27, 34, 34, 34, 51, 27, 45, 25, 45, 27, 51, 34, 66, 66, 51, 51, 45, 45, 45, 45, 51, 51, 66, 66, 66, 99, 51, 85, 45, 81, 45, 85, 51, 99, 66, 130

Offset: 0

N. J. A. Sloane, Jul 08 2016

			The array begins:
4, 6, 6, 10, 10, 18, 18, 34, 34, 66, 66, 130, 130, ...
4, 6, 6, 10, 10, 18, 18, 34, 34, 66, 66, 130, 130, ...
6, 9, 9, 15, 15, 27, 27, 51, 51, 99, 99, 195, 195, ...
6, 9, 9, 15, 15, 27, 27, 51, 51, 99, 99, 195, 195, ...
10, 15, 15, 25, 25, 45, 45, 85, 85, 165, 165, 325, 325, ...
10, 15, 15, 25, 25, 45, 45, 85, 85, 165, 165, 325, 325, ...
18, 27, 27, 45, 45, 81, 81, 153, 153, 297, 297, 585, 585, ...
...

The main diagonal is conjectured to be A183978. Cf. A274635, A274637.

cp's OEIS Frontend

A274638 Main diagonal of A274637.

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A274636 Square array read by antidiagonals: T(m,n) (m>=0, n>=0) = (2^floor(m/2)+1)*(2^ceiling(n/2)+1).

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