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%I A373908 #12 Jun 22 2024 14:11:55
%S A373908 1,1,2,9,38,136,452,1495,5031,17114,58282,198032,671856,2278870,
%T A373908 7731892,26238839,89047335,302191369,1025487338,3479970844,
%U A373908 11809261583,40074827170,135994407483,461498426696,1566098800484,5314568565096,18035031128780,61202027710656
%N A373908 Number of compositions of 7*n into parts 2 and 7.
%H A373908 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-20,35,-35,21,-7,1).
%F A373908 a(n) = A369813(7*n).
%F A373908 a(n) = Sum_{k=0..floor(n/2)} binomial(n+5*k,n-2*k).
%F A373908 a(n) = 7*a(n-1) - 20*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7).
%F A373908 G.f.: 1/(1 - x - x^2/(1 - x)^6).
%o A373908 (PARI) a(n) = sum(k=0, n\2, binomial(n+5*k, n-2*k));
%Y A373908 Cf. A373907, A373909, A373910, A373911, A373912.
%Y A373908 Cf. A109961, A369840, A373904.
%Y A373908 Cf. A369813.
%K A373908 nonn,easy
%O A373908 0,3
%A A373908 _Seiichi Manyama_, Jun 22 2024

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