login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A181133 a(n) = n + A003056(n). 1
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..n-1} A042974(k). - R. J. Mathar, Oct 08 2010

G.f.: (2*x-1)/(1-x)^2 + Theta_2(0,sqrt(x))/(x^(1/8)*(2-2*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 re-fitted to something precise, sequence extended beyond a(15), and comment added by R. J. Mathar, Oct 24 2010

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 8 20:37 EST 2021. Contains 349596 sequences. (Running on oeis4.)