This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A067988 #22 Aug 30 2025 17:13:31
%S A067988 1,3,10,25,60,133,284,585,1175,2310,4464,8502,15995,29775,54920,
%T A067988 100487,182556,329555,591550,1056405,1877821,3323868,5860800,10297500,
%U A067988 18033925,31487643,54824854,95211205,164948700,285121105,491804144,846631137,1454746355,2495275650
%N A067988 Row sums of triangle A067330; also of triangle A067418.
%C A067988 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
%F A067988 a(n) = (n+2)*((3*n+5)*F(n+1)+(n+1)*F(n))/10, with F(n) := A000045(n) (Fibonacci).
%F A067988 G.f.: (1+x^2)/(1-x-x^2)^3.
%F A067988 Sum_{j=0..n} binomial(n-j,j)*n*j/2. - _Zerinvary Lajos_, Oct 19 2006
%F A067988 E.g.f.: exp(x/2)*(5*(10 + 18*x + 7*x^2)*cosh(sqrt(5)*x/2) + sqrt(5)*(14 + 46*x + 15*x^2)*sinh(sqrt(5)*x/2))/50. - _Stefano Spezia_, Aug 30 2025
%p A067988 a:=n->sum(binomial(n-j,j)*n*j/2,j=0..n): seq(a(n), n=2..30); # _Zerinvary Lajos_, Oct 19 2006
%t A067988 Table[((n+2)((3n+5)Fibonacci[n+1]+(n+1)Fibonacci[n]))/10,{n,0,30}] (* _Harvey P. Dale_, Feb 02 2020 *)
%Y A067988 Cf. A000045, A001628, A067330, A067418.
%K A067988 nonn,easy,changed
%O A067988 0,2
%A A067988 _Wolfdieter Lang_, Feb 15 2002
%E A067988 a(29)-a(33) from _Stefano Spezia_, Aug 30 2025