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A067988 Row sums of triangle A067330; also of triangle A067418. 3
1, 3, 10, 25, 60, 133, 284, 585, 1175, 2310, 4464, 8502, 15995, 29775, 54920, 100487, 182556, 329555, 591550, 1056405, 1877821, 3323868, 5860800, 10297500, 18033925, 31487643, 54824854, 95211205, 164948700 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

a(n) is the sum of the positions of the 0's in all Fibonacci binary words of length n+1. A Fibonacci binary word is a binary word having no 00 subword. Example: a(3)=25 because the Fibonacci binary words of length 4 are 1110, 1111, 1101, 1010, 1011, 0110, 0111 and 0101, the positions of the 0's being 4, 3, 2, 4, 2, 1, 4, 1, 1 and 3 (their sum is 25). - Emeric Deutsch, Jan 04 2009

LINKS

Table of n, a(n) for n=0..28.

FORMULA

a(n)= (n+2)*((3*n+5)*F(n+1)+(n+1)*F(n))/10, with F(n) := A000045(n) (Fibonacci).

G.f.: (1+x^2)/(1-x-x^2)^3.

Sum_{j=0..n} binomial(n-j,j)*n*j/2. - Zerinvary Lajos, Oct 19 2006

MAPLE

a:=n->sum(binomial(n-j, j)*n*j/2, j=0..n): seq(a(n), n=2..30); # Zerinvary Lajos, Oct 19 2006

CROSSREFS

Cf. A001628.

Sequence in context: A000247 A097763 A034506 * A297186 A262380 A005674

Adjacent sequences:  A067985 A067986 A067987 * A067989 A067990 A067991

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, Feb 15 2002

STATUS

approved

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Last modified January 25 07:25 EST 2020. Contains 331241 sequences. (Running on oeis4.)