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A023665
Convolution of A000201 and A023533.
2
1, 3, 4, 7, 11, 13, 17, 20, 23, 28, 32, 37, 43, 47, 52, 57, 61, 67, 71, 77, 84, 90, 97, 103, 109, 117, 122, 129, 136, 141, 149, 155, 161, 169, 175, 184, 192, 199, 209, 215, 224, 232, 240, 249, 256, 264, 274, 280, 289, 297, 304, 314, 321, 329, 337
OFFSET
1,2
FORMULA
a(n) = Sum_{j=1..n} A000201(j) * A023533(n-j+1).
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

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Last modified September 20 15:43 EDT 2024. Contains 376073 sequences. (Running on oeis4.)