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A124920
Location of record values in A080577; also partial sums of A006128 plus 1.
2
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
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
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