The On-Line Encyclopedia of Integer Sequences (OEIS)

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A028574

Expansion of 1/((1-16*x)^2*(1 - 14*x + 56*x^2 - 64*x^3)).
(history; published version)

#18 by Charles R Greathouse IV at Thu Sep 08 08:44:50 EDT 2022

PROG

(MAGMAMagma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( 1/((1-16*x)^2*(1-14*x+56*x^2-64*x^3)) )); // G. C. Greubel, May 28 2019

Discussion

Thu Sep 08

08:44

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

#17 by N. J. A. Sloane at Sat Jun 01 17:10:39 EDT 2019

STATUS

proposed

approved

#16 by Jon E. Schoenfield at Tue May 28 23:23:16 EDT 2019

STATUS

editing

proposed

#15 by Jon E. Schoenfield at Tue May 28 23:23:14 EDT 2019

NAME

Expansion of 1/((1-16*x)^2*(1 - 14*x + 56*x^2 - 64*x^3)).

FORMULA

E.g.f.: (3 - 98*exp(2*x) + 1176*exp(6*x) + 128*(-5 + 168*x)*exp(14*x) )*exp(2*x)/441. (End)

STATUS

proposed

editing

#14 by G. C. Greubel at Tue May 28 13:40:55 EDT 2019

STATUS

editing

proposed

#13 by G. C. Greubel at Tue May 28 13:39:49 EDT 2019

NAME

Expansion of 1/((1-16*x-1)^2*(1-14*x+56*x^2-64*x^3)).

COMMENTS

The original o.g.f. was transferred to a new sequence A308436.

LINKS

G. C. Greubel, <a href="/A028574/b028574.txt">Table of n, a(n) for n = 0..820</a>

FORMULA

From G. C. Greubel, May 28 2019: (Start)

a(n) = 2^n*(3 - 49*2^(n+1) + 147*2^(2*n+3) + (21*n -10)*2^(3*n+6))/441.

E.g.f.: (3 - 98*exp(2*x) + 1176*exp(6*x) + 128*(-5 + 168*x)*exp(14*x) )*exp(2*x)/441. (End)

MATHEMATICA

CoefficientList[Series[1/((1-16*x)^2*(1-14*x+56*x^2-64*x^3)), {x, 0, 20}], x] (* G. C. Greubel, May 28 2019 *)

PROG

(PARI) my(x='x+O('x^20)); Vec(1/((1-16*x)^2*(1-14*x+56*x^2-64*x^3))) \\ G. C. Greubel, May 28 2019

(MAGMA) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( 1/((1-16*x)^2*(1-14*x+56*x^2-64*x^3)) )); // G. C. Greubel, May 28 2019

(Sage) (1/((1-16*x)^2*(1-14*x+56*x^2-64*x^3))).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, May 28 2019

EXTENSIONS

G.f. corrected by Georg Fischer, May 27 2019

STATUS

proposed

editing

#12 by Sean A. Irvine at Mon May 27 18:27:21 EDT 2019

STATUS

editing

proposed

#11 by Sean A. Irvine at Mon May 27 18:27:15 EDT 2019

NAME

Expansion of 1/((16x16*x-1)^2*(1-14x14*x+56x56*x^2-64x64*x^3)).

STATUS

proposed

editing

#10 by Jon E. Schoenfield at Mon May 27 16:23:57 EDT 2019

STATUS

editing

proposed

#9 by Jon E. Schoenfield at Mon May 27 16:23:51 EDT 2019

AUTHOR

N. J. A. Sloane.

STATUS

proposed

editing