%I #12 Sep 08 2022 08:45:15

%S 1,3,7,15,31,31,63,159,383,863,1855,2847,4863,9951,22207,49823,109183,

%T 200287,355903,674335,1384959,2979295,6473151,12882335,24271231,

%U 45849951,90168639,185506079,392646911,804881631,1581561023,3048759455

%N Expansion of (1+2*x+4*x^2+8*x^3+16*x^4)/(1-x-32*x^6).

%H G. C. Greubel, <a href="/A098583/b098583.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,32).

%F a(n) = a(n-1) + 32*a(n-6).

%F a(n) = Sum_{k=0..n} binomial(n-k, floor(k/5)) * 2^k.

%t CoefficientList[Series[(1+2x+4x^2+8x^3+16x^4)/(1-x-32x^6),{x,0,40}],x] (* or *) LinearRecurrence[{1,0,0,0,0,32},{1,3,7,15,31,31},40] (* _Harvey P. Dale_, May 02 2014 *)

%o (PARI) x='x+O('x^30); Vec((1+2*x+4*x^2+8*x^3+16*x^4)/(1-x-32*x^6)) \\ _G. C. Greubel_, Feb 03 2018

%o (Magma) I:=[1,3,7,15,31,31]; [n le 6 select I[n] else Self(n-1) + 32*Self(n-6): n in [1..30]]; // _G. C. Greubel_, Feb 03 2018

%Y Cf. A098582.

%K easy,nonn

%O 0,2

%A _Paul Barry_, Sep 16 2004