login
A110113
Diagonal sums of A083856.
2
0, 1, 2, 3, 5, 9, 17, 34, 71, 154, 346, 802, 1914, 4693, 11800, 30379, 79963, 214925, 589223, 1645994, 4681037, 13541446, 39817560, 118925810, 360577616, 1109158545, 3459636358, 10936941299, 35026082521, 113588037953
OFFSET
0,3
COMMENTS
Sums of antidiagonals of A083856.
LINKS
A. G. Shannon and J. V. Leyendekkers, The Golden Ratio family and the Binet equation, Notes on Number Theory and Discrete Mathematics, 21(2) (2015), 35-42.
FORMULA
a(n) = Sum_{k = 0..n} ((1 + sqrt(4*(n - k) + 1))/2)^k / sqrt(4*(n - k) + 1) - ((1 -sqrt(4*(n - k) + 1))/2)^k / sqrt(4*(n - k) + 1). [Corrected by Petros Hadjicostas, Dec 26 2019]
MAPLE
T := proc(n, k) local v; option remember; if 0 <= n and k = 0 then v := 0; end if; if 0 <= n and k = 1 then v := 1; end if; if 0 <= n and 2 <= k then v := T(n, k - 1) + n*T(n, k - 2); end if; v; end proc;
a := proc(n) local k; add(T(n - k, k), k = 0 .. n); end proc;
seq(a(n), n = 0..40); # Petros Hadjicostas, Dec 26 2019
CROSSREFS
Sequence in context: A061902 A166286 A179807 * A341960 A137155 A014227
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Jul 12 2005
STATUS
approved