A099132 - OEIS

%I #21 Mar 05 2019 09:11:36

%S 1,1,1,1,1,1,2,7,22,57,127,253,464,804,1354,2289,4005,7372,14198,

%T 28033,55523,108699,208982,394555,734561,1357136,2504932,4643816,

%U 8671852,16313856,30855957,58502733,110882143,209689343,395358538,743376838

%N Quintisection of 1/(1-x^5-x^6).

%H Seiichi Manyama, <a href="/A099132/b099132.txt">Table of n, a(n) for n = 0..3646</a>

%H V. C. Harris, C. C. Styles, <a href="http://www.fq.math.ca/Scanned/2-4/harris.pdf">A generalization of Fibonacci numbers</a>, Fib. Quart. 2 (1964) 277-289, sequence u(n,1,5).

%H V. E. Hoggatt, Jr., <a href="/A005676/a005676.pdf">7-page typed letter to N. J. A. Sloane with suggestions for new sequences</a>, circa 1977.

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1,1)

%F G.f.: (1-x)^4/((1-x)^5-x^6);

%F a(n) = Sum_{k=0..n} binomial(k, 5(n-k));

%F a(n) = 5a(n-1)-10a(n-2)+10a(n-3)-5a(n-4)+a(n-5)+a(n-6);

%F a(n) = A017837(5n).

%F a(n) = Sum_{k=0..floor(n/5)} binomial(n-k, 5k). - _Paul Barry_, May 09 2005

%t LinearRecurrence[{5,-10,10,-5,1,1},{1,1,1,1,1,1},40] (* _Harvey P. Dale_, Aug 20 2012 *)

%o (PARI) Vec((1-x)^4/((1-x)^5-x^6) + O(x^40)) \\ _Michel Marcus_, Sep 06 2017

%Y Cf. A005676, A017837.

%K easy,nonn

%O 0,7

%A _Paul Barry_, Sep 29 2004