OFFSET
1,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..5000
FORMULA
T(n, k) = Sum_{j=1..n} A000201(k+1 +binomial(n+2,3) -binomial(j+2,3)), for 0 <= k <= n*(n+3)/2, n >= 1 (as an irregular triangle). - G. C. Greubel, Jul 18 2022
MATHEMATICA
Table[Sum[Floor[(k+1 +Binomial[n+2, 3] -Binomial[j+2, 3])*GoldenRatio], {j, n}], {n, 7}, {k, 0, n*(n+3)/2}] (* G. C. Greubel, Jul 18 2022 *)
PROG
(Magma)
A023533:= func< n | Binomial(Floor((6*n-1)^(1/3)) +2, 3) ne n select 0 else 1 >;
[(&+[Floor(k*(1+Sqrt(5))/2)*A023533(n-k+1): k in [1..n]]): n in [1..80]]; // G. C. Greubel, Jul 18 2022
(SageMath)
def A023665(n, k): return sum( floor((k+1 + binomial(n+2, 3) - binomial(j+2, 3))*golden_ratio) for j in (1..n) )
flatten([[A023665(n, k) for k in (0..n*(n+3)/2)] for n in (1..7)]) # G. C. Greubel, Jul 18 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved