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

0,2

Links

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

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)

Example

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

Prog

(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

Crossrefs

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

Cf. A001045, A081254, A138238.

Sequence in context: A339401 A316601 A341263 * A071245 A297744 A091968

Adjacent sequences: A178744 A178745 A178746 * A178748 A178749 A178750

Keyword

nonn

Author

David Scambler, Jun 09 2010

Extensions

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

Status

approved