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A178747
Sum of terms in 'rows' of A178746.
3
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
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).
Sequence in context: A339401 A316601 A341263 * A071245 A297744 A091968
KEYWORD
nonn
AUTHOR
David Scambler, Jun 09 2010
EXTENSIONS
Terms a(16) and beyond from Andrew Howroyd, Mar 03 2020
STATUS
approved