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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.)