A082505 -id:A082505 - cp's OEIS frontend

A173078 a(n) = (52^n - 2(-1)^n - 9)/3.

1, 3, 11, 23, 51, 103, 211, 423, 851, 1703, 3411, 6823, 13651, 27303, 54611, 109223, 218451, 436903, 873811, 1747623, 3495251, 6990503, 13981011, 27962023, 55924051, 111848103, 223696211, 447392423, 894784851, 1789569703, 3579139411

Offset: 1

Paul Curtz, Feb 09 2010

The sequence and higher-order differences in subsequent rows are
    1,  3,  11,  23, 51, 103, 211, 423, 851, 1703, 3411, 6823, 13651
    2,  8,  12,  28, 52, 108, 212, 428, 852, 1708, 3412, 6828, 13652
    6,  4,  16,  24, 56, 104, 216, 424, 856, 1704, 3416, 6824, 13656
   -2,  12,  8,  32, 48, 112, 208, 432, 848, 1712, 3408, 6832, 13648
   14,  -4, 24,  16, 64,  96, 224, 416, 864, 1696, 3424, 6816, 13664
  -18,  28, -8,  48, 32, 128, 192, 448, 832, 1728, 3392, 6848,  1363
   46, -36, 56, -16, 96,  64, 256, 384, 896, 1664, 3456, 6784,  1369
The main diagonal 1,8,16,... is essentially A000079.
A subdiagonal is 2, 4, 8, 16, ... A155559.
Other diagonals are 3, 12, 24, 48, ... = 3*A151821, 6, 12, 24, ... = A082505 and -2, -4, -8, -16, ..., a negated variant of A171449.

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (2,1,-2).

List([1..40], n-> (5*2^n - 2*(-1)^n - 9)/3); # G. C. Greubel, Dec 01 2019

[5*2^n/3-2*(-1)^n/3-3: n in [1..40]]; // Vincenzo Librandi, Aug 05 2011

seq( (5*2^n -2*(-1)^n -9)/3, n=1..40); # G. C. Greubel, Dec 01 2019

LinearRecurrence[{2,1,-2},{1,3,11},40] (* Harvey P. Dale, Oct 01 2018 *)

vector(40, n, (5*2^n - 2*(-1)^n - 9)/3) \\ G. C. Greubel, Dec 01 2019

[(5*2^n - 2*(-1)^n - 9)/3 for n in (1..40)] # G. C. Greubel, Dec 01 2019

a(n) = 2*a(n-1) + a(n-2) - 2*a(n-3).
a(n+1) - 2*a(n) = A010686(n-1).
a(n) = A084214(n+1) - 3.
G.f.: x*(1 + x + 4*x^2) / ( (1-x)*(1-2*x)*(1+x) ).
a(2n+3) - a(2n+1) = 10*A000302(n).
E.g.f.: (-2*exp(-x) + 6 - 9*exp(x) + 5*exp(2*x))/3. - G. C. Greubel, Dec 01 2019

A176414 Expansion of (7+8x)/(1+2x).

Original entry on oeis.org

7, -6, 12, -24, 48, -96, 192, -384, 768, -1536, 3072, -6144, 12288, -24576, 49152, -98304, 196608, -393216, 786432, -1572864, 3145728, -6291456, 12582912, -25165824, 50331648, -100663296, 201326592, -402653184, 805306368

Offset: 0

Klaus Brockhaus, Apr 17 2010

Inverse binomial transform of A176415.

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (-2).

Cf. A176415, A110164 (essentially the same), A122803.

Join[{7},NestList[-2#&,-6,40]] (* Harvey P. Dale, Jun 20 2020 *)

{for(n=0, 29, print1(polcoeff((7+8*x)/(1+2*x)+x*O(x^n), n), ", "))}

A176414(n)=3*(-2)^n+!n*4 \\ M. F. Hasler, Apr 19 2015

a(n) = A110164(n+2) for n > 0.
a(n) = 3*(-2)^n = 3*A122803(n+1) for n > 0; a(0) = 7.
a(n) = -2*a(n-1) for n > 1; a(0) = 7, a(1) = -6.
a(n) = (-1)^n*A132477(n) = (-1)^n*A122391(n+3), n>1.
a(n) = (-1)^n*A111286(n+2) = (-1)^n*A098011(n+4) = (-1)^n*A091629(n) = (-1)^n*A087009(n+3) = (-1)^n*A082505(n+1) = (-1)^n*A042950(n+1) = (-1)^n*A007283(n) = (-1)^n*A003945(n+1), n>0. - R. J. Mathar, Dec 10 2010
E.g.f.: 4 + 3*exp(-2*x). - Alejandro J. Becerra Jr., Feb 15 2021

Edited by M. F. Hasler, Apr 19 2015

cp's OEIS Frontend

A173078 a(n) = (52^n - 2(-1)^n - 9)/3.

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A176414 Expansion of (7+8x)/(1+2x).

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cp's OEIS Frontend

A173078 a(n) = (5*2^n - 2*(-1)^n - 9)/3.

Views

Author

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Comments

Links

Programs

GAP

Magma

Maple

Mathematica

PARI

Sage

Formula

A176414 Expansion of (7+8*x)/(1+2*x).

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Mathematica

PARI

PARI

Formula

Extensions

A173078 a(n) = (52^n - 2(-1)^n - 9)/3.

A176414 Expansion of (7+8x)/(1+2x).