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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
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 (list; graph; refs; listen; history; text; internal format)
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: A230411 A029128 A303660 * A070941 A061775 A225634

Adjacent sequences:  A290018 A290019 A290020 * A290022 A290023 A290024

KEYWORD

nonn,easy

AUTHOR

David A. Corneth, Aug 25 2017

STATUS

approved

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Last modified June 25 04:09 EDT 2021. Contains 345452 sequences. (Running on oeis4.)