A178747 Sum of terms in 'rows' of A178746.

1, 3, 19, 65, 295, 1129, 4663, 18441, 74359, 296585, 1188727, 4751497, 19015543, 76048521, 304232311, 1216874633, 4867651447, 19470387337, 77882161015, 311527770249, 1246113527671, 4984450615433, 19937812248439, 79751235012745, 319004979197815, 1276019860867209

Offset: 0

Author

David Scambler, Jun 09 2010

Keywords

• nonn

Examples

			a(0) = 1, a(1) = 3, a(2) = 6 + 6 + 7 = 19.
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..500

Crossrefs

Cf. A178748 (sum of '1' bits in rows of A178746).

Cf. A001045, A081254, A138238.

Programs

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

PARI

a(n) = {(17*4^n + 5*(2*(-1)^n-1)*2^n - 7*(-1)^n)/15} \\ Andrew Howroyd, Mar 03 2020

Formula

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]

From David Scambler, Jun 17 2010: (Start)

a(n) = (17*4^n + 5*(2*(-1)^n-1)*2^n - 7*(-1)^n)/15.

a(n) = A001045(n+1) * A081254(n+1) + (-1)^n * A138238(n-1).

(End)

Extensions

Terms a(16) and beyond from Andrew Howroyd, Mar 03 2020