A156591 -id:A156591 - cp's OEIS frontend

A157823 a(n) = A156591(n) + A156591(n+1).

-5, -1, -2, -4, -8, -16, -32, -64, -128, -256, -512, -1024, -2048, -4096, -8192, -16384, -32768, -65536, -131072, -262144, -524288, -1048576, -2097152, -4194304, -8388608, -16777216, -33554432, -67108864, -134217728, -268435456, -536870912, -1073741824

Offset: 0

Paul Curtz, Mar 07 2009

A156591 = 2,-7,6,-8,4,-12,... a(n) is companion to A154589 = 4,-1,-2,-4,-8,.For this kind ,companion of sequence b(n) is first differences a(n), second differences being b(n). Well known case: A131577 and A011782. a(n)+b(n)=A000079 or -A000079. a(n)=A154570(n+2)-A154570(n) ,A154570 = 1,3,-4,2,-6,-2,-14,. See sequence(s) identical to its p-th differences (A130785,A130781,A024495,A000749,A138112(linked to Fibonacci),A139761).

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

Vec(-(9*x-5)/(2*x-1) + O(x^100)) \\ Colin Barker, Feb 03 2015

a(n) = 2*a(n-1) for n>1. G.f.: -(9*x-5) / (2*x-1). - Colin Barker, Feb 03 2015

Edited by Charles R Greathouse IV, Oct 11 2009

A156605 a(n) = (4^n + 20)/3.

Original entry on oeis.org

7, 8, 12, 28, 92, 348, 1372, 5468, 21852, 87388, 349532, 1398108, 5592412, 22369628, 89478492, 357913948, 1431655772, 5726623068, 22906492252, 91625968988, 366503875932, 1466015503708, 5864062014812, 23456248059228, 93824992236892, 375299968947548

Offset: 0

Paul Curtz, Feb 11 2009

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (5, -4).

Cf. A002450, A154879, A156591.

[(4^n+20)/3: n in [0..35]]; // Vincenzo Librandi, Jul 24 2011

(4^Range[0,40] + 20)/3 (* G. C. Greubel, Jun 25 2021 *)

[(4^n + 20)/3 for n in (0..40)] # G. C. Greubel, Jun 25 2021

a(n) = -A156591(2n+1).
a(n) = 4 + A154879(2n) = 7 + A002450(n).
a(n) = 4*a(n-1) - 20, n > 0.
G.f.: (7 - 27*x)/((1-x)*(1-4*x)). - R. J. Mathar, Feb 23 2009
E.g.f.: (1/3)*(20*exp(x) + exp(4*x)). - G. C. Greubel, Jun 25 2021

Edited and extended by R. J. Mathar, Feb 23 2009

cp's OEIS Frontend

A157823 a(n) = A156591(n) + A156591(n+1).

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A156605 a(n) = (4^n + 20)/3.

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