A152950 a(n) = 3 + n*(n-1)/2.

3, 4, 6, 9, 13, 18, 24, 31, 39, 48, 58, 69, 81, 94, 108, 123, 139, 156, 174, 193, 213, 234, 256, 279, 303, 328, 354, 381, 409, 438, 468, 499, 531, 564, 598, 633, 669, 706, 744, 783, 823, 864, 906, 949, 993, 1038, 1084, 1131, 1179, 1228, 1278, 1329, 1381, 1434, 1488

Offset

1,1

Comments

a(1)=3; then add 1 to the first number, then 2, 3, 4, ... and so on.

Numbers m such that 8*m - 23 is a square. - Bruce J. Nicholson, Jul 25 2017

Alternating sums of 3 consecutive terms of A152948 give this sequence. The a(n) are never divisible by primes listed in A191065. - Klaus Purath, Jan 22 2026

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Ângela Mestre and José Agapito, Square Matrices Generated by Sequences of Riordan Arrays, J. Int. Seq., Vol. 22 (2019), Article 19.8.4.

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Formula

a(n) = A152949(n+1) = 3 + A000217(n-1). - R. J. Mathar, Jan 03 2009

a(n) = 3 + C(n,2), n >= 1. - Zerinvary Lajos, Mar 12 2009

a(n) = a(n-1) + n - 1 (with a(1)=3). - Vincenzo Librandi, Nov 27 2010

Sum_{n>=1} 1/a(n) = 2*Pi*tanh(sqrt(23)*Pi/2)/sqrt(23). - Amiram Eldar, Dec 13 2022

From Elmo R. Oliveira, Nov 18 2024: (Start)

G.f.: x*(3 - 5*x + 3*x^2)/(1-x)^3.

E.g.f.: exp(x)*(3 + x^2/2) - 3.

a(n) = A027691(n-1)/2.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 3. (End)

a(n) = 2*a(n-1) - a(n-2) + 1 for n >= 3. - Klaus Purath, Jan 22 2026

Maple

A152950:=n->3 + n*(n-1)/2; seq(A152950(n), n=1..100); # Wesley Ivan Hurt, Jan 28 2014

Mathematica

s=3; lst={3}; Do[s+=n; AppendTo[lst, s], {n, 1, 5!}]; lst
Table[3 + n*(n-1)/2, {n, 100}] (* Wesley Ivan Hurt, Jan 28 2014 *)

Prog

(SageMath) [3+binomial(n, 2) for n in range(1, 55)] # Zerinvary Lajos, Mar 12 2009
(PARI) a(n)=3+n*(n-1)/2 \\ Charles R Greathouse IV, Oct 07 2015
(Magma) [3+n*(n-1)/2 : n in [1..50]]; // Wesley Ivan Hurt, Mar 25 2020

Crossrefs

Cf. A000124, A000217, A027691, A152947, A152948, A152949.

Sequence in context: A355697 A167928 A090867 * A391230 A005626 A227561

Adjacent sequences: A152947 A152948 A152949 * A152951 A152952 A152953

Keyword

nonn,easy

Author

Vladimir Joseph Stephan Orlovsky, Dec 15 2008

Status

approved