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 A152948 a(n) = (n^2 - 3*n + 6)/2. 23
 2, 2, 3, 5, 8, 12, 17, 23, 30, 38, 47, 57, 68, 80, 93, 107, 122, 138, 155, 173, 192, 212, 233, 255, 278, 302, 327, 353, 380, 408, 437, 467, 498, 530, 563, 597, 632, 668, 705, 743, 782, 822, 863, 905, 948, 992, 1037, 1083, 1130, 1178, 1227, 1277, 1328, 1380 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS a(1) = 2; then add 0 to the first number, then 1, 2, 3, 4, ... and so on. Essentially the same as A022856, A089071 and A133263. - R. J. Mathar, Dec 19 2008 First differences are A001477. If we ignore the zero polygonal numbers, then for n >= 3, a(n) is the minimal k such that the k-th n-gonal number is a sum of two n-gonal numbers (see formula and example). - Vladimir Shevelev, Jan 20 2014 Numbers m such that 8m - 15 is a square. - Bruce J. Nicholson, Jul 24 2017 LINKS Michael De Vlieger, Table of n, a(n) for n = 1..10000 Marilena Barnabei, Flavio Bonetti, Niccolò Castronuovo, and Matteo Silimbani, Permutations avoiding a simsun pattern, The Electronic Journal of Combinatorics (2020) Vol. 27, Issue 3, P3.45. E. R. Berlekamp, A contribution to mathematical psychometrics, Unpublished Bell Labs Memorandum, Feb 08 1968 [Annotated scanned copy] Kyu-Hwan Lee and Se-jin Oh, Catalan triangle numbers and binomial coefficients, arXiv:1601.06685 [math.CO], 2016. 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) = a(n-1) + n-2 (with a(1)=2). - Vincenzo Librandi, Nov 26 2010 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). G.f.: -x*(2 - 4*x + 3*x^2) /  (x-1)^3. - R. J. Mathar, Oct 30 2011 If the zero polygonal numbers are ignored, then for n >= 4, the a(n)-th n-gonal number is a sum of the (a(n)-1)-th n-gonal number and the (n-1)-th n-gonal number. - Vladimir Shevelev, Jan 20 2014 EXAMPLE a(7)=17. This means that the 17th (positive) heptagonal number 697 (cf. A000566) is the smallest heptagonal number which is a sum of two (positive) heptagonal numbers. We have 697 = 616 + 81 with indices 17, 16, 6 in A000566. - Vladimir Shevelev, Jan 20 2014 MATHEMATICA Array[(#^2 - 3 # + 6)/2 &, 54] (* or *) Rest@ CoefficientList[Series[-x (2 - 4 x + 3 x^2)/(x - 1)^3, {x, 0, 54}], x] (* Michael De Vlieger, Mar 25 2020 *) PROG (Sage) [2+binomial(n, 2) for n in range(0, 54)] # Zerinvary Lajos, Mar 12 2009 (MAGMA) [ (n^2-3*n+6)/2: n in [1..60] ]; (PARI) a(n)=(n^2-3*n+6)/2 \\ Charles R Greathouse IV, Sep 28 2015 CROSSREFS Cf. A000124, A000217, A152947. Sequence in context: A179523 A087729 A039890 * A018136 A243853 A293419 Adjacent sequences:  A152945 A152946 A152947 * A152949 A152950 A152951 KEYWORD nonn,easy AUTHOR Vladimir Joseph Stephan Orlovsky, Dec 15 2008 STATUS approved

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Last modified April 15 07:23 EDT 2021. Contains 342975 sequences. (Running on oeis4.)