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%I #6 Nov 28 2020 20:01:03
%S 1,2,7,11,25,35,65,85,140,175,266,322,462,546,750,870,1155,1320,1705,
%T 1925,2431,2717,3367,3731,4550,5005,6020,6580,7820,8500,9996,10812,
%U 12597,13566,15675,16815,19285,20615,23485,25025,28336,30107,33902
%N Sequence resulting from a sum of three repeated binomial(n+3,4) sequences.
%C Euler transform of length 3 sequence [2,k,-1] with k=4 (cf. A028724 for k=3). - _Georg Fischer_, Nov 28 2020
%F a(1) = b(1), a(2) = b(2), a(n) = b(n) + b(n-1) + b(n-2) for n > 2, where k = 4 and b(n) = binomial(floor((n+7)/2), k) = A189976(n-7).
%e b(n) = 1, 1, 5, 5, 15, 15, 35, 35, 70, 70,126,126
%e + 0, 1, 1, 5, 5, 15, 15, 35, 35, 70, 70,126
%e + 0, 0, 1, 1, 5, 5, 15, 15, 35, 35, 70, 70
%e -----------------------------------------------
%e a(n) = 1, 2, 7, 11, 25, 35, 65, 85,140,175,266,322
%t k := 4; nmax := 32; a := Flatten[Table[{Binomial[n,k], Binomial[n,k]},{n,k,nmax}]];
%t a + Flatten[Join[{0}, Drop[a,-1]]] + Flatten[Join[{0,0}, Drop[a,-2]]] (* _Georg Fischer_, Nov 29 2020 *)
%Y Cf. A001651(k=1), A001318(k=2), A028724(k=3).
%Y Cf. repeated binomial coefficients: A008805(k=2), A058187(k=3), A189976(k=4).
%K nonn,easy
%O 1,2
%A _Alford Arnold_, May 08 2004
%E More terms from and edited by _Georg Fischer_, Nov 28 2020
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