A257418 -id:A257418

Search: a257418 -id:a257418

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A343175

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

+10
4

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,1

COMMENTS

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

LINKS

Harvey P. Dale, Table of n, a(n) for n = 0..1000

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

FORMULA

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)

MATHEMATICA

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

CROSSREFS

Cf. A257418, A085601, A343176.

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Apr 26 2021

EXTENSIONS

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

STATUS

approved

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.

+10
2

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,1

COMMENTS

A342759 is the main sequence for this entry.

LINKS

Table of n, a(n) for n=0..30.

Rémy Sigrist, Illustration of initial terms

Rémy Sigrist, C# program for A342761

FORMULA

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

EXAMPLE

See illustration in Links section.

PROG

(C#) See Links section.

CROSSREFS

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]

KEYWORD

nonn

AUTHOR

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

STATUS

approved

A343176

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

+10
2

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,1

COMMENTS

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

LINKS

Table of n, a(n) for n=0..26.

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

FORMULA

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)

CROSSREFS

Cf. A257418, A036562, A343175.

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Apr 26 2021

EXTENSIONS

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

STATUS

approved

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