A106464 Antidiagonal sums of number triangle A003989.

1, 1, 2, 3, 3, 4, 6, 6, 5, 11, 6, 9, 15, 12, 8, 18, 9, 21, 22, 15, 11, 32, 20, 18, 27, 31, 14, 45, 15, 32, 36, 24, 41, 57, 18, 27, 43, 60, 20, 66, 21, 51, 72, 33, 23, 84, 42, 60, 57, 61, 26, 81, 67, 88, 64, 42, 29, 135, 30, 45, 105

Offset

0,3

Comments

Consider the triangle T(n, k) = A003989(n, k) = gcd(n-k+1, k), n >= 1, k = 1..n. Then a(n) = Sum_{k=0..floor(n/2)} T(n-k+1, k+1), for n >= 0. - R. J. Mathar, May 11 2018 [adjusted to the definition of A003989. - Wolfdieter Lang, May 12 2018]

Links

Robert Israel, Table of n, a(n) for n = 0..10000

Formula

a(n) = Sum_{k=0..floor(n/2)} gcd(n-2*k+1, k+1). [corrected by R. J. Mathar, May 11 2018]

Maple

f:= n -> add(igcd(n-2*k+1, k+1), k=0..n/2):
map(f, [$0..100]); # Robert Israel, May 11 2018

Mathematica

Array[Sum[GCD[# - 2 k + 1, k + 1], {k, 0, Floor[#/2]}] &, 61, 0] (* Michael De Vlieger, May 14 2018 *)

Prog

(PARI) a(n) = sum(k=0, n\2, gcd(n-2*k+1, k+1)); \\ Michel Marcus, May 11 2018
(GAP) Flat(List([0..70], n->Sum([0..Int(n/2)], k->Gcd(n-2*k+1, k+1)))); # Muniru A Asiru, May 15 2018

Crossrefs

Cf. A003989, A106466.

Sequence in context: A257241 A239964 A290585 * A093003 A348540 A118096

Adjacent sequences: A106461 A106462 A106463 * A106465 A106466 A106467

Keyword

easy,nonn

Author

Paul Barry, May 03 2005

Extensions

Name corrected by R. J. Mathar, May 11 2018

Status

approved