A143982 - OEIS

%I #12 May 27 2020 07:17:29

%S 0,0,1,4,10,20,36,64,120,240,496,1024,2080,4160,8255,16368,32504,

%T 64464,126940,246640,470536,879056,1607862,2886800,5117800,9046960,

%U 16166475,29666676,56666754,113330260,236315636,507817728,1109184992,2433554624,5318390075

%N Binomial transform of A079261.

%H Alois P. Heinz, <a href="/A143982/b143982.txt">Table of n, a(n) for n = 1..1000</a>

%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>

%F a(n) = Sum_{k=3..n} C(n,k)*A079261(k).

%e a(11) = [165,330,462,462,330,165,55,11,1] * [1,0,0,0,1,0,0,0,1] = 165+330+1 = 496.

%p bintrans:= proc(p) proc(n) add(p(k) *binomial(n,k), k=0..n) end end:

%p f:= proc(n) if isprime(n) and modp(n,4)=3 then 1 else 0 fi end:

%p a:= bintrans(f):

%p seq(a(n), n=1..40);

%t a[n_] := Sum[Binomial[n, k] Boole[PrimeQ[k] && Mod[k, 4] == 3], {k, 3, n}];

%t Array[a, 40] (* _Jean-François Alcover_, May 27 2020 *)

%Y Cf. A007318, A079261.

%K nonn

%O 1,4

%A _Alois P. Heinz_, Sep 06 2008