The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A115113 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A115113

a(n) = 3*a(n-1) + 4*a(n-2), with a(0) = 2, a(1) = 6, a(2) = 10.
(history; published version)

#24 by Charles R Greathouse IV at Thu Sep 08 08:45:23 EDT 2022

PROG

(MAGMAMagma) I:=[6, 10]; [2] cat [n le 2 select I[n] else 3*Self(n-1) + 4*Self(n-2): n in [1..49]]; // G. C. Greubel, Nov 23 2018

Discussion

Thu Sep 08

08:45

OEIS Server: https://oeis.org/edit/global/2944

#23 by Alois P. Heinz at Tue May 10 13:21:01 EDT 2022

STATUS

editing

approved

#22 by Alois P. Heinz at Tue May 10 13:19:47 EDT 2022

DATA

2, 6, 10, 54, 202, 822, 3274, 13110, 52426, 209718, 838858, 3355446, 13421770, 53687094, 214748362, 858993462, 3435973834, 13743895350, 54975581386, 219902325558, 879609302218, 3518437208886, 14073748835530, 56294995342134, 225179981368522, 900719925474102

#21 by Alois P. Heinz at Tue May 10 13:17:40 EDT 2022

NAME

a(n) = 3*a(n-1) + 4*a(n-2), with a(0) = 2, a(1) = 6, a(2) = 10.

STATUS

approved

editing

Discussion

Tue May 10

13:18

Alois P. Heinz: this was removed in an old edit ... but is needed here ...

#20 by Alois P. Heinz at Tue May 10 13:16:55 EDT 2022

NAME

a(n) = 3*a(n-1) + 4*a(n-2), with a(-1) = 3, a(0) = -2, a(1) = 6.

DATA

3, -2, 6, 10, 54, 202, 822, 3274, 13110, 52426, 209718, 838858, 3355446, 13421770, 53687094, 214748362, 858993462, 3435973834, 13743895350, 54975581386, 219902325558, 879609302218, 3518437208886, 14073748835530, 56294995342134

OFFSET

-1,0,1

FORMULA

a(n) = (-2*(7*(-1)^n - 2^(1 + 2*n)))/5 for n >= -1 0.

a(n) = 3*a(n-1) + 4*a(n-2) for n > 02.

From Paul Curtz, May 10 2022: (Start)

a(n-1) + a(n) = 4^n for n >= 0. (End)

CROSSREFS

Cf. A000302.

KEYWORD

sign,nonn,easy,changed

STATUS

editing

approved

#19 by Alois P. Heinz at Tue May 10 13:10:00 EDT 2022

STATUS

proposed

editing

Discussion

Tue May 10

13:16

Alois P. Heinz: the chanes are destructive ... will revert ...

#18 by Paul Curtz at Tue May 10 12:48:01 EDT 2022

STATUS

editing

proposed

Discussion

Tue May 10

13:10

Alois P. Heinz: the value of a(0) was changed from 2 to -2.   So the g.f. and e.g.f. and programs are no longer correct or consistent.   The b-file is no longer correct.  Is there any reason for this?  No reason can be seen.  You introduced many inconsistencies ... this cannot be published ...

#17 by Paul Curtz at Tue May 10 12:46:45 EDT 2022

NAME

a(n) = 3*a(n-1) + 4*a(n-2), with a(-1) = 3, a(0) = -2, a(1) = 6.

DATA

OFFSET

0,-1,1

FORMULA

a(n) = (-2*(7*(-1)^n - 2^(1 + 2*n)))/5 for n >= 0-1.

a(n) = 3*a(n-1) + 4*a(n-2) for n > 10.

a(-1) =3.

a(n-1) + a(n) = 4^n for n >= 0. (endEnd)

STATUS

proposed

editing

#16 by Paul Curtz at Tue May 10 12:21:10 EDT 2022

STATUS

editing

proposed

#15 by Paul Curtz at Tue May 10 12:18:16 EDT 2022

NAME

a(n) = 3*a(n-1) + 4*a(n-2), with a(0) = -2, a(1) = 6.

DATA

-2, 6, 10, 54, 202, 822, 3274, 13110, 52426, 209718, 838858, 3355446, 13421770, 53687094, 214748362, 858993462, 3435973834, 13743895350, 54975581386, 219902325558, 879609302218, 3518437208886, 14073748835530, 56294995342134

FORMULA

a(n) = (-2*(7*(-1)^n - 2^(1 + 2*n)))/5 for n > = 0.

a(n) = 3*a(n-1) + 4*a(n-2) for n > 2.1

From Paul Curtz, May 10 2022: (Start)

a(-1) =3.

a(n-1) + a(n) = 4^n for n >= 0. (end)

CROSSREFS

Cf. A000302.

KEYWORD

nonn,sign,easy

STATUS

approved

editing