A257418 -id:A257418 - cp's OEIS frontend

A343175 a(0)=2; for n > 0, a(n) = 2^(2*n-1) + 2^n + 1.

2, 5, 13, 41, 145, 545, 2113, 8321, 33025, 131585, 525313, 2099201, 8392705, 33562625, 134234113, 536903681, 2147549185, 8590065665, 34360000513, 137439477761, 549756862465, 2199025352705, 8796097216513, 35184380477441, 140737505132545, 562949986975745, 2251799880794113

Offset: 0

N. J. A. Sloane, Apr 26 2021

A bisection of A257418. Apart from first term, same as A085601.

Harvey P. Dale, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (7,-14,8).

Cf. A257418, A085601, A343176.

LinearRecurrence[{7,-14,8},{2,5,13,41},30] (* Harvey P. Dale, Aug 04 2024 *)

From Chai Wah Wu, Apr 26 2021: (Start)
a(n) = 7*a(n-1) - 14*a(n-2) + 8*a(n-3) for n > 3.
G.f.: (-4*x^3 - 6*x^2 + 9*x - 2)/((x - 1)*(2*x - 1)*(4*x - 1)). (End)

a(18)-a(26) from Martin Ehrenstein, Apr 26 2021

A342761 Fold a square sheet of paper alternately vertically to the left and horizontally downwards; after each fold, draw a line along each inward crease; after n folds, the resulting graph has a(n) edges.

Original entry on oeis.org

4, 7, 10, 15, 25, 43, 79, 147, 283, 547, 1075, 2115, 4195, 8323, 16579, 33027, 65923, 131587, 262915, 525315, 1050115, 2099203, 4197379, 8392707, 16783363, 33562627, 67121155, 134234115, 268460035, 536903683, 1073790979

Offset: 0

Rémy Sigrist and N. J. A. Sloane, Mar 22 2021

nonn

A342759 is the main sequence for this entry.

			See illustration in Links section.

Rémy Sigrist, Illustration of initial terms
Rémy Sigrist, C# program for A342761

Cf. A342759.

It appears that a(n) = A257418(n) + 2 for n >= 2. Hugo Pfoertner, Mar 29 2021 [This is true - N. J. A. Sloane, Apr 26 2021]

Theorem: a(2*t) = 2^(2*t)+3*2^(t-1)+3 for t >= 1; a(2*t+1) = 2^(2*t+1)+2^(t+1)+3 for t >= 0. - N. J. A. Sloane, Apr 26 2021

A343176 a(0)=3; for n > 0, a(n) = 2^(2n) + 32^(n-1) + 1.

Original entry on oeis.org

3, 8, 23, 77, 281, 1073, 4193, 16577, 65921, 262913, 1050113, 4197377, 16783361, 67121153, 268460033, 1073790977, 4295065601, 17180065793, 68719869953, 274878693377, 1099513200641, 4398049656833, 17592192335873, 70368756760577, 281475001876481, 1125899957174273, 4503599728033793

Offset: 0

N. J. A. Sloane, Apr 26 2021

A bisection of A257418. Apart from first term, same as A036562.

Index entries for linear recurrences with constant coefficients, signature (7,-14,8).

Cf. A257418, A036562, A343175.

From Chai Wah Wu, Apr 26 2021: (Start)
a(n) = 7*a(n-1) - 14*a(n-2) + 8*a(n-3) for n > 3.
G.f.: -(4*x - 3)*(x^2 + 3*x - 1)/((x - 1)*(2*x - 1)*(4*x - 1)). (End)

a(17)-a(26) from Martin Ehrenstein, Apr 26 2021

cp's OEIS Frontend

A343175 a(0)=2; for n > 0, a(n) = 2^(2*n-1) + 2^n + 1.

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A342761 Fold a square sheet of paper alternately vertically to the left and horizontally downwards; after each fold, draw a line along each inward crease; after n folds, the resulting graph has a(n) edges.

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Formula

A343176 a(0)=3; for n > 0, a(n) = 2^(2n) + 32^(n-1) + 1.

Views

Author

Keywords

Comments

Links

Crossrefs

Formula

Extensions

cp's OEIS Frontend

A343175 a(0)=2; for n > 0, a(n) = 2^(2*n-1) + 2^n + 1.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

Formula

Extensions

A342761 Fold a square sheet of paper alternately vertically to the left and horizontally downwards; after each fold, draw a line along each inward crease; after n folds, the resulting graph has a(n) edges.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

A343176 a(0)=3; for n > 0, a(n) = 2^(2*n) + 3*2^(n-1) + 1.

Views

Author

Keywords

Comments

Links

Crossrefs

Formula

Extensions

A343176 a(0)=3; for n > 0, a(n) = 2^(2n) + 32^(n-1) + 1.