A322072 Row sums of the triangle A322071.

2, 6, 12, 22, 37, 62, 98, 155, 240, 370, 563, 856, 1287, 1936, 2901, 4335, 6462, 9617, 14281, 21181, 31371, 46405, 68568, 101221, 149279, 219983, 323922, 476635, 700881, 1030010, 1512829, 2220797, 3258451, 4778710, 7005172, 10264722, 15035060, 22014172

Offset

1,1

Comments

Conjecture: The difference a(n + 1) - a(n) between two consecutive terms is not a perfect square except for n = 1, 5 and 6.

Links

Robert Israel, Table of n, a(n) for n = 1..2000

Formula

a(n) = Sum_{k=1..n} floor(2*n^k/k^k).

a(n) = Sum_{k=1..n} floor(A005843(n^k/A000312(k))).

Maple

a := n -> sum(floor(2*n^k/k^k), k = 1 .. n): seq(a(n), n = 1 .. 40)

Mathematica

a[n_]:=Sum[Floor[2*(n/k)^k], {k, 1, n}]; Array[a, 40]

Prog

(Maxima) a(n):=sum(floor(2*n^k/k^k), k, 1, n)$ makelist(a(n), n, 0, 40);
(PARI)
a(n) = sum(k=1, n, floor(2*n^k/k^k));
vector(40, n, a(n))
(GAP) List([1..40], n->Sum([1..n], k->Int(2*n^k/k^k))); # Muniru A Asiru, Nov 25 2018
(Magma) [(&+[Floor(2*(n/k)^k): k in [1..n]]): n in [1..40]]; // G. C. Greubel, Nov 25 2018
(Sage) [sum(floor(2*(n/k)^k) for k in (1..n)) for n in (1..40)] # G. C. Greubel, Nov 25 2018

Crossrefs

Cf. A000312, A005843, A322071.

Sequence in context: A232234 A045964 A005819 * A304627 A168193 A182977

Adjacent sequences: A322069 A322070 A322071 * A322073 A322074 A322075

Keyword

nonn

Author

Stefano Spezia, Nov 25 2018

Status

approved