



2, 3, 5, 6, 7, 9, 10, 11, 12, 14, 15, 16, 17, 18, 20, 21, 22, 23, 24, 25, 27, 28, 29, 30, 31, 32, 33, 35, 36, 37, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 77, 78, 79, 80, 81, 82, 83, 84, 85
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

Obtained starting with a triangle with 1's and a trailing 2, and accumulating a partial sum along rows and columns:
2; # 2
1,2; # 3,5
1,1,2; # 6,7,9
1,1,1,2; # 10,11,12,14
1,1,1,1,2; # 15,16,17,18,20
1,1,1,1,1,2;


LINKS

Robert Israel, Table of n, a(n) for n = 1..10000


FORMULA

a(n) = 2 + Sum_{k=1..n1} A042974(k).  R. J. Mathar, Oct 08 2010
G.f.: (2*x1)/(1x)^2 + Theta_2(0,sqrt(x))/(x^(1/8)*(22*x)) where Theta_2 is a Jacobi theta function.  Robert Israel, Dec 24 2017


MAPLE

A003056:= [seq(n$(n+1), n=1..20)]:
A003056+[$1..nops(A003056)]; # Robert Israel, Dec 24 2017


MATHEMATICA

Array[# + Floor[(Sqrt[1 + 8 #]  1)/2] &, 74] (* Michael De Vlieger, Dec 24 2017 *)


PROG

(PARI) a(n) = n + floor((sqrt(1+8*n)1)/2) \\ Iain Fox, Dec 25 2017


CROSSREFS

Cf. A003056, A042974.
Sequence in context: A175140 A039144 A183864 * A136432 A039105 A187328
Adjacent sequences: A181130 A181131 A181132 * A181134 A181135 A181136


KEYWORD

nonn,easy


AUTHOR

Craig Michoski (michoski(AT)google.com), Oct 05 2010


EXTENSIONS

Definition refitted to something precise, sequence extended beyond a(15), and comment added by R. J. Mathar, Oct 24 2010


STATUS

approved



