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A121776
Antidiagonal sums of triangle A121775.
1
1, 1, 3, 6, 10, 16, 23, 36, 52, 76, 118, 181, 271, 427, 675, 1057, 1686, 2705, 4318, 6923, 11142, 17966, 28999, 46793, 75522, 122018, 197254, 318907, 515616, 833796, 1348542, 2181304, 3528487, 5707947, 9234075, 14938991, 24169111, 39103056, 63265607, 102359886
OFFSET
0,3
FORMULA
a(n) = Sum_{k=0..[n/2]} Sum_{d|(n-k)} phi((n-k)/d)*C(d,k) for n>0, with a(0)=1.
MATHEMATICA
a[0] = 1; a[n_] := Sum[DivisorSum[n-k, EulerPhi[(n-k)/#] * Binomial[#, k] &], {k, 0, Floor[n/2]}]; Array[a, 50, 0] (* Amiram Eldar, Aug 15 2023 *)
PROG
(PARI) a(n)=if(n==0, 1, sum(k=0, n\2, sumdiv(n-k, d, eulerphi((n-k)/d)*binomial(d, k))))
CROSSREFS
Sequence in context: A011913 A024531 A034198 * A310085 A310086 A310087
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Aug 23 2006
STATUS
approved