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A145018 a(1) = 4; then add 1 to the first number, then 2, then 3 and so on. 8
4, 5, 7, 10, 14, 19, 25, 32, 40, 49, 59, 70, 82, 95, 109, 124, 140, 157, 175, 194, 214, 235, 257, 280, 304, 329, 355, 382, 410, 439, 469, 500, 532, 565, 599, 634, 670, 707, 745, 784, 824, 865, 907, 950, 994, 1039, 1085, 1132, 1180, 1229, 1279, 1330, 1382, 1435, 1489, 1544, 1600, 1657, 1715, 1774, 1834, 1895, 1957, 2020, 2084, 2149, 2215 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Numbers m such that 8m-31 is a square. - Bruce J. Nicholson, Jul 25 2017

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..1000

Augustine O. Munagi, Integer Compositions and Higher-Order Conjugation, J. Int. Seq., Vol. 21 (2018), Article 18.8.5.

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

FORMULA

a(n) = (n^2 - n + 8)/2. - Benoit Cloitre.

From R. J. Mathar, Oct 01 2008: (Start)

G.f.: x*(4 -7*x +4*x^2)/(1-x)^3.

a(n) = a(n-1) + n - 1.

a(n) = 4 + A000217(n-1). (End)

a(n) = 4 + C(n,2), n>=1. - Zerinvary Lajos, Mar 12 2009

MAPLE

A145018:=n->(n^2 - n + 8)/2: seq(A145018(n), n=1..100); # Wesley Ivan Hurt, Jul 25 2017

MATHEMATICA

Nest[Append[#, #[[-1]] + Length@ #] &, {4}, 66] (* or *)

Rest@ CoefficientList[Series[x (4 - 7 x + 4 x^2)/(1 - x)^3, {x, 0, 67}], x] (* Michael De Vlieger, Jan 23 2019 *)

PROG

(Sage)[4+binomial(n, 2) for n in xrange(1, 68)] # Zerinvary Lajos, Mar 12 2009

(PARI) x='x+O('x^50); Vec(x*(4 -7*x +4*x^2)/(1-x)^3) \\ G. C. Greubel, Feb 18 2017

CROSSREFS

Cf. A000217.

Sequence in context: A234141 A093517 A248858 * A018910 A022936 A057708

Adjacent sequences:  A145015 A145016 A145017 * A145019 A145020 A145021

KEYWORD

nonn,easy

AUTHOR

Jayanth (mergujayanth(AT)yahoo.com), Sep 29 2008

EXTENSIONS

More terms from Alexander R. Povolotsky, Sep 29 2008

Edited by Benoit Cloitre and R. J. Mathar, Sep 30 2008

STATUS

approved

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Last modified December 7 05:14 EST 2019. Contains 329839 sequences. (Running on oeis4.)