OFFSET
1,2
COMMENTS
Rising diagonal sums of triangle A011973, taken with rows as centered text.
LINKS
Index entries for linear recurrences with constant coefficients, signature (1,0,2,0,0,-1).
FORMULA
a(n) = Sum_{k=0..floor((n-1)/3)} (binomial(2*n-2-5*k,k) + binomial(2*n-3-5*k,k)) for n >= 2; a(1)=1. - John Molokach, Jul 11 2013
a(n) = a(n-1) + 2*a(n-3) - a(n-6), starting with {1, 2, 2, 3, 7, 11}. - T. D. Noe, Jul 11 2013
G.f.: x*(1+x-x^3)/(1-x-2*x^3+x^6) - John Molokach, Jul 15 2013
a(n) = Sum_{k=0..floor((2n-1)/3)} binomial(2n-k-2-3*floor(k/2),floor(k/2)). - John Molokach, Jul 29 2013
EXAMPLE
a(1) = 1;
a(2) = 1 + 1;
a(3) = 1 + 1;
a(4) = 1 + 1 + 1;
a(5) = 1 + 1 + 3 + 2;
a(6) = 1 + 1 + 5 + 4;
a(7) = 1 + 1 + 7 + 6 + 1;
a(8) = 1 + 1 + 9 + 8 + 6 + 3;
a(9) = 1 + 1 + 11 + 10 + 15 + 10;
a(10) = 1 + 1 + 13 + 12 + 28 + 21 + 1.
MATHEMATICA
LinearRecurrence[{1, 0, 2, 0, 0, -1}, {1, 2, 2, 3, 7, 11}, 40] (* T. D. Noe, Jul 11 2013 *)
PROG
(PARI) a(n) = if(n<=1, 1, sum(k=0, floor((n-1)/3), binomial(2*n-2-5*k, k)+binomial(2*n-1-5*k, k)) ); \\ Joerg Arndt, Jul 11 2013
CROSSREFS
KEYWORD
nonn
AUTHOR
John Molokach, Jul 09 2013
STATUS
approved