OFFSET
0,6
COMMENTS
The Le1{1,5} and Le2{5,1} triangle sums of Sierpinski’s triangle A047999 equal this sequence; see the formulas for their definitions. The Le1{1,5} and Le2{5,1} triangle sums are similar to the Kn11 and Kn21 sums, the Ca1 and Ca2 sums, and the Gi1 and Gi2 sums, see A180662.
Some A191373(2^n-p) sequences, 0<=p<=32, lead to known sequences, see the crossrefs.
LINKS
Sam Northshield, Sums across Pascal’s triangle modulo 2, Congressus Numerantium, 200, pp. 35-52, 2010.
FORMULA
a(2*n) = a(n) and a(2*n+1) = a(n) + a(n-2) with a(0) = 1, a(1) = 1 and a(n)=0 for n<=-1.
a(n) = Le1{1,5}(n) = add(T(n-4*k,k),k=0..floor(n/5))
a(n) = Le1{1,5}(n) = sum(binomial(i + j, i) mod 2 | (i + 5*j) = n)
a(n) = Le2{5,1}(n) = add(T(n-4*k,n-5*k),k=0..floor(n/5))
a(n) = Le2{5,1}(n) = sum(binomial(i + j, i) mod 2 | (5*i + j) = n)
G.f.: Product_{n>=0} (1+x^(2^n)+x^(5*2^n)).
G.f. A(x) satisfies: A(x) = (1 + x + x^5) * A(x^2). - Ilya Gutkovskiy, Jul 09 2019
MAPLE
CROSSREFS
KEYWORD
nonn
AUTHOR
Johannes W. Meijer, Jun 05 2011
STATUS
approved