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A113439 a(n) = a(n-1) + Sum_{k=1..floor(n/4)} a(n-4k), with a(0)=1.

%I A113439 #13 Jul 08 2024 21:32:01
%S A113439 1,1,1,1,2,3,4,5,8,12,17,23,34,50,72,101,146,212,306,436,627,905,1305,
%T A113439 1871,2689,3872,5577,8014,11521,16576,23858,34309,49337,70968,102108,
%U A113439 146868,211233,303832,437080,628708,904306,1300737,1871065,2691401
%N A113439 a(n) = a(n-1) + Sum_{k=1..floor(n/4)} a(n-4k), with a(0)=1.
%C A113439 If presented in four rows a(4k), a(4k+1), a(4k+2) and a(4k+3), each term is the sum of the previous term in the sequence and the partial sum of its row; see Example section.
%H A113439 G. C. Greubel, <a href="/A113439/b113439.txt">Table of n, a(n) for n = 0..1000</a>
%H A113439 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,2,-1).
%F A113439 a(n) = a(n-1) + 2*a(n-4) - a(n-5).
%F A113439 a(n) = 9*a(n-4) - 28*a(n-8) + 38*a(n-12) - 20*a(n-16) +a(n-20).
%F A113439 G.f.: (1-x^4)/(1-x-2*x^4+x^5).
%e A113439 From _Jon E. Schoenfield_, Mar 11 2017: (Start)
%e A113439 Table of values T(j,k) = a(4k+j) in 4 rows:
%e A113439 .
%e A113439   j | k=0     1     2     3     4     5     6     7
%e A113439 ----+--------------------------------------------------
%e A113439   0 |   1     2     8    34   146   627  2689 11521 ...
%e A113439   1 |   1     3    12    50   212   905  3872 16576 ...
%e A113439   2 |   1     4    17    72   306  1305  5577 23858 ...
%e A113439   3 |   1     5    23   101   436  1871  8014 34309 ...
%e A113439 .
%e A113439     T(2,4) = T(1,4) + T(2,0) + T(2,1) + T(2,2) + T(2,3)
%e A113439       306  =   212  +    1   +    4   +   17   +   72
%e A113439 (End)
%t A113439 CoefficientList[Series[(1 - x^4)/(1 - x - 2*x^4 + x^5), {x,0,50}], x] (* _G. C. Greubel_, Mar 11 2017 *)
%t A113439 LinearRecurrence[{1,0,0,2,-1},{1,1,1,1,2},50] (* _Harvey P. Dale_, Nov 10 2019 *)
%o A113439 (PARI) x='x+O('x^50); Vec((1-x^4)/(1-x-2*x^4+x^5)) \\ _G. C. Greubel_, Mar 11 2017
%Y A113439 Cf. A028495, A113435, A113444.
%K A113439 nonn,easy
%O A113439 0,5
%A A113439 _Floor van Lamoen_, Nov 04 2005