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

1,2

Links

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

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

Example

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 ...

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

Crossrefs

Cf. A000041, A006128, A080577.

Sequence in context: A225947 A330909 A281969 * A064934 A227637 A171985

Adjacent sequences: A124917 A124918 A124919 * A124921 A124922 A124923

Keyword

easy,nonn

Author

Alford Arnold, Nov 13 2006

Extensions

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

Clarification of name from Ilya Gutkovskiy, Apr 04 2017

Status

approved