A124920 Location of record values in A080577; also partial sums of A006128 plus 1.

1, 2, 5, 11, 23, 43, 78, 132, 218, 346, 538, 813, 1212, 1768, 2548, 3616, 5079, 7044, 9688, 13186, 17816, 23868, 31767, 41973, 55147, 71998, 93520, 120814, 155359, 198812, 253375, 321510, 406437, 511803, 642265, 803141, 1001155, 1243967

Offset: 1

Author

Alford Arnold, Nov 13 2006

Keywords

• easy
• nonn

Examples

			A080577 begins
1
2 11
3 21 111
4 31 22 211 1111
5 41 32 311 221 2111 11111
6 51 42 411 33 321 3111 222 2211 21111 111111
therefore A124920 begins 1 2 5 11 23 ...
		

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000041, A006128, A080577.

Programs

Maple

A008284 := proc(n,k) if n >= 1 and n = k or k = 1 then 1 elif k > n then 0 else add( A008284(n-k,i),i=1..k) ; fi ; end: A006128 := proc(n) add( k*A008284(n,k),k=1..n) ; end: a := 1 : printf("%d,",a) ; for n from 2 to 80 do a := a + A006128(n-1) : printf("%d,",a) ; od : # R. J. Mathar, Jan 13 2007

Formula

A124920(n) = A124920(n-1)+ A006128(n-1), n>1; a(1) = 1.

G.f.: x/(1 - x) + Sum_{i>=1} i*x^(i+1)/(1 - x) * Product_{j=1..i} 1/(1 - x^j). - Ilya Gutkovskiy, Apr 04 2017

a(n) ~ exp(Pi*sqrt(2*n/3)) * (log(6*n) + 2*gamma - 2*log(Pi)) * sqrt(3) / (4*Pi^2), where gamma is the Euler-Mascheroni constant (A001620). - Vaclav Kotesovec, May 19 2018

Extensions

More terms from R. J. Mathar, Jan 13 2007

Clarification of name from Ilya Gutkovskiy, Apr 04 2017