A344435 a(n) = Sum_{k=1..n} (A000292(n) mod A000217(k)).

0, 1, 5, 4, 17, 35, 13, 35, 102, 93, 114, 148, 205, 168, 331, 435, 370, 604, 600, 539, 844, 1139, 1102, 1230, 1314, 1393, 1660, 1974, 2438, 1957, 3000, 3472, 2584, 3632, 4076, 3217, 3039, 4936, 4799, 4558, 6909, 6915, 6296, 7180, 9406, 7040, 9736, 10535, 6569, 10122, 12316, 11111, 12037, 13961

Offset

1,3

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Formula

a(n) = Sum_{k=1..n} (binomial(n+2,3) mod binomial(k+1,2)).

Example

A000292(7) = 84 and A000217(1..7) are 1,3,6,10,15,21,28, so a(7) = (84 mod 1) + (84 mod 3) + ... + (84 mod 28) = 0+0+0+4+9+0+0 = 13.

Maple

f:= proc(n) local t, j;
  t:= binomial(n+2, 3);
  add(t mod binomial(j+1, 2), j=2..n)
end proc:
map(f, [$1..100]);

Prog

(PARI) a(n) = sum(k=1, n, binomial(n+2, 3) % binomial(k+1, 2)); \\ Michel Marcus, May 19 2021

Crossrefs

Cf. A000217, A000292.

Sequence in context: A282225 A282202 A190728 * A100791 A056883 A006747

Adjacent sequences: A344432 A344433 A344434 * A344436 A344437 A344438

Keyword

nonn

Author

J. M. Bergot and Robert Israel, May 19 2021

Status

approved