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A178747 Sum of terms in 'rows' of A178746.

%I A178747 #10 Mar 04 2020 03:25:02
%S A178747 1,3,19,65,295,1129,4663,18441,74359,296585,1188727,4751497,19015543,
%T A178747 76048521,304232311,1216874633,4867651447,19470387337,77882161015,
%U A178747 311527770249,1246113527671,4984450615433,19937812248439,79751235012745,319004979197815,1276019860867209
%N A178747 Sum of terms in 'rows' of A178746.
%H A178747 Andrew Howroyd, <a href="/A178747/b178747.txt">Table of n, a(n) for n = 0..500</a>
%F A178747 G.f: (1/4)*x^3 - (1/8)*x^2 - 1/16 + (x^4 + (3/4)*x^3 - (1/2)*x^2 - (3/16)*x + 1/16)*F(x) = 0. [From GUESSS]
%F A178747 From _David Scambler_, Jun 17 2010: (Start)
%F A178747 a(n) = (17*4^n + 5*(2*(-1)^n-1)*2^n - 7*(-1)^n)/15.
%F A178747 a(n) = A001045(n+1) * A081254(n+1) + (-1)^n * A138238(n-1).
%F A178747 (End)
%e A178747 a(0) = 1, a(1) = 3, a(2) = 6 + 6 + 7 = 19.
%o A178747 (PARI) seq(n)={my(a=vector(n+1), f=0, p=0, k=1, s=0); while(k<=#a, my(b=bitxor(p+1,p)); f=bitxor(f,b); p=bitxor(p, bitand(b,f)); if(p>2^k, a[k]=s; k++; s=0); s+=p); a} \\ _Andrew Howroyd_, Mar 03 2020
%o A178747 (PARI) a(n) = {(17*4^n + 5*(2*(-1)^n-1)*2^n - 7*(-1)^n)/15} \\ _Andrew Howroyd_, Mar 03 2020
%Y A178747 Cf. A178748 (sum of '1' bits in rows of A178746).
%Y A178747 Cf. A001045, A081254, A138238.
%K A178747 nonn
%O A178747 0,2
%A A178747 _David Scambler_, Jun 09 2010
%E A178747 Terms a(16) and beyond from _Andrew Howroyd_, Mar 03 2020