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A008936 Expansion of (1 - 2*x -x^4) / (1 - 2*x)^2 in powers of x. 1
1, 2, 4, 8, 15, 28, 52, 96, 176, 320, 576, 1024, 1792, 3072, 5120, 8192, 12288, 16384, 16384, 0, -65536, -262144, -786432, -2097152, -5242880, -12582912, -29360128, -67108864, -150994944, -335544320, -738197504 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..30.

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

FORMULA

a(n) = 2^n for all n<4. - Michael Somos, Aug 19 2014

a(n) = 4*(a(n-1) - a(n-2)) for all n in Z except n=4. - Michael Somos, Aug 19 2014

a(n) = 2*a(n-1) - 2^(n-4) = 2^n - (n-3) * 2^(n-4) for all n>=4. - Michael Somos, Aug 19 2014

0 = a(n)*(-8*a(n+1) + 8*a(n+2) - 2*a(n+3)) + a(n+1)*(+4*a(n+1) - 4*a(n+2) + a(n+3)) for all n in Z. - Michael Somos, Aug 19 2014

EXAMPLE

G.f. = 1 + 2*x + 4*x^2 + 8*x^3 + 15*x^4 + 28*x^5 + 52*x^6 + 96*x^7 + 176*x^8 + ...

MAPLE

A008936 := proc(n) option remember; if n <= 3 then 2^n else 2*A008936(n-1)-2^(n-4); fi; end;

MATHEMATICA

a[ n_] := 2^n - 2^(n-4) Max[0, n-3]; (* Michael Somos, Aug 19 2014 *)

PROG

(PARI) {a(n) = 2^n - 2^(n-4) * max(n-3, 0)}; /* Michael Somos, 12 Jan 2000 */

(PARI) Vec((1-2*x-x^4)/(1-2*x)+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012

CROSSREFS

Sequence in context: A114833 A065617 A062065 * A320452 A073769 A008937

Adjacent sequences:  A008933 A008934 A008935 * A008937 A008938 A008939

KEYWORD

sign,easy

AUTHOR

N. J. A. Sloane, Alejandro Teruel (teruel(AT)usb.ve)

EXTENSIONS

Better description from Michael Somos, Jan 12 2000.

STATUS

approved

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Last modified February 16 21:59 EST 2019. Contains 320200 sequences. (Running on oeis4.)