A290021 a(0) = 1; for n > 0, a(n) = a(k) + a(m) where binomial(k + m + 2, 2) - m = n and binomial(k + m + 2, 2) is the smallest triangular number larger than or equal to m.

1, 2, 3, 3, 4, 4, 4, 4, 5, 5, 4, 5, 5, 6, 5, 5, 5, 6, 6, 6, 6, 5, 5, 6, 7, 6, 7, 6, 5, 5, 6, 7, 7, 7, 7, 6, 5, 6, 6, 7, 7, 8, 7, 7, 6, 6, 6, 7, 7, 7, 8, 8, 7, 7, 7, 6, 5, 7, 8, 7, 8, 8, 8, 7, 8, 7, 5, 6, 6, 8, 8, 8, 8, 8, 8, 8, 8, 6, 6, 6, 7, 7, 8, 9, 8, 8, 8

Offset

0,2

Links

Rémy Sigrist, Table of n, a(n) for n = 0..10000

Formula

a(n+1) = a(A002262(n)) + a(A025581(n)). - Rémy Sigrist, Feb 12 2021

Example

a(0) = 1.
a(1) = a(0) + a(0) = 1 + 1 = 2.
a(2) = a(0) + a(1) = 1 + 2 = 3.
a(3) = a(1) + a(0) = 2 + 1 = 3.
a(4) = a(0) + a(2) = 1 + 3 = 4.
a(5) = a(1) + a(1) = 2 + 2 = 4.
a(6) = a(2) + a(0) = 3 + 1 = 4.

Prog

(PARI) a(n) = {if(n==0, return(1)); my(s = ceil((-3 + sqrt(8*n+1))/ 2), b = binomial(s+2, 2), k = b - n, m = s - k); a(k) + a(m)}
(PARI) a=vector(87); print1(a[u=1]=1); for (d=1, oo, for (n=1, d, print1(", "a[u++]=a[n]+a[d+1-n]); if (u==87, break (2)))) \\ Rémy Sigrist, Feb 12 2021

Crossrefs

Cf. A002262, A025581.

Sequence in context: A358372 A029128 A303660 * A348020 A070941 A061775

Adjacent sequences: A290018 A290019 A290020 * A290022 A290023 A290024

Keyword

nonn,easy

Author

David A. Corneth, Aug 25 2017

Status

approved