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A247281 4^n -(-1)^n. 5
0, 5, 15, 65, 255, 1025, 4095, 16385, 65535, 262145, 1048575, 4194305, 16777215, 67108865, 268435455, 1073741825, 4294967295, 17179869185, 68719476735, 274877906945, 1099511627775, 4398046511105, 17592186044415 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Numerators of the first and second upper diagonals of the array

0, 0, 0, 5/4, 5/2, 75/16, 125/16,... = b(n)/c(n)

0, 0, 5/4, 5/4, 35/16, 25/8, 325/64,...

0, 5/4, 0, 15/16, 15/16, 125/64, 190/64,...

5/4, -5/4, 15/16, 0, 65/64, 65/64, 515/256,...

-5/2, 35/16, -15/16, 65/64, 0, 255/256, 255/256,...

etc.

The denominators of the first row are c(n) = 1 followed by A084623(n).

The inverse binomial transform of b(n)/c(n) is (-1)^(n+1)*b(n)/c(n). The main diagonal is 0's=A000004. These two characteristics of the difference array show that the first row is an autosequence of the first kind.

a(n) mod 9 is a sequence of period 6: repeat 0, 5, 6, 2, 3, 8.

LINKS

Table of n, a(n) for n=0..22.

Index entries for linear recurrences with constant coefficients, signature (3,4).

OEIS Wiki, Autosequence

FORMULA

a(n) = 5*A015521(n).

a(n+1) = 10*A037481(n) +5.

a(n+1) = 4*a(n) + 5*(-1)^n.

a(n) = 3*a(n-1) + 4*a(n-2). - Colin Barker, Sep 11 2014

G.f.: -5*x / ((x+1)*(4*x-1)). - Colin Barker, Sep 11 2014

MATHEMATICA

LinearRecurrence[{3, 4}, {0, 5}, 23] (* Jean-François Alcover, May 22 2016 *)

PROG

(PARI) concat(0, Vec(-5*x / ((x+1)*(4*x-1)) + O(x^100))) \\ Colin Barker, Sep 11 2014

(PARI) vector(100, n, 4^(n-1)+(-1)^n) \\ Derek Orr, Sep 11 2014

CROSSREFS

Cf. A000351, A015521, A037481, A084623.

Sequence in context: A149620 A149621 A149622 * A149623 A149624 A149625

Adjacent sequences: A247278 A247279 A247280 * A247282 A247283 A247284

KEYWORD

nonn,easy

AUTHOR

Paul Curtz, Sep 11 2014

EXTENSIONS

Typos in data fixed by Colin Barker, Sep 11 2014

STATUS

approved

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Last modified December 5 19:04 EST 2022. Contains 358588 sequences. (Running on oeis4.)