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 A022267 a(n) = n*(9*n + 1)/2. 17
 0, 5, 19, 42, 74, 115, 165, 224, 292, 369, 455, 550, 654, 767, 889, 1020, 1160, 1309, 1467, 1634, 1810, 1995, 2189, 2392, 2604, 2825, 3055, 3294, 3542, 3799, 4065, 4340, 4624, 4917, 5219, 5530, 5850, 6179 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS From Floor van Lamoen, Jul 21 2001: (Start) Write 0, 1, 2, 3, 4, ... in a triangular spiral; then a(n) is the sequence found by reading the line from 0 in the direction 0, 5, ... . The spiral begins: .             15             / \           16  14           /     \         17   3  13         /   / \   \       18   4   2  12       /   /     \   \     19   5   0---1  11     /   /             \   20   6---7---8---9--10 . (End) a(n) is the sum of n consecutive integers starting from 4*n+1: (5), (9+10), (13+14+15), ... - Klaus Purath, Jul 07 2020 a(n) with n>0 are the numbers with the periodic length 3 in the Bulgarian and Mancala solitaire. - Paul Weisenhorn, Jan 29 2022 LINKS Lei Zhou, Table of n, a(n) for n = 0..10000 Milan Janjic, Two Enumerative Functions Leo Tavares, Illustration: X Triangles Index entries for linear recurrences with constant coefficients, signature (3,-3,1). FORMULA a(n) = A110449(n, 4) for n>3. From Bruno Berselli, Feb 11 2011: (Start) G.f.: x*(5 + 4*x)/(1 - x)^3. a(n) = 4*A000217(n) + A000566(n). (End) a(n) = 9*n + a(n-1) - 4 with n>0, a(0)=0. - Vincenzo Librandi, Aug 04 2010 a(n) = A218470(9*n+4). - Philippe Deléham, Mar 27 2013 a(n) = A000217(5*n) - A000217(4*n). - Bruno Berselli, Oct 13 2016 E.g.f.: (1/2)*(9*x^2 + 10*x)*exp(x). - G. C. Greubel, Jul 17 2017 a(n) = A060544(n+1) - A016813(n). - Leo Tavares, Mar 20 2022 MAPLE seq(binomial(9*n+1, 2)/9, n=0..37); # Zerinvary Lajos, Jan 21 2007 MATHEMATICA Table[ n (9 n + 1)/2, {n, 0, 40}] (* or *) LinearRecurrence[{3, -3, 1}, {0, 5, 19}, 40] (* Harvey P. Dale, Jul 01 2013 *) PROG (PARI) vector(100, n, (n-1)*(9*n-8)/2) \\ Derek Orr, Feb 06 2015 CROSSREFS Cf. A000217, A051682, A110449, A235332. Cf. numbers of the form n*(d*n+10-d)/2: A008587, A056000, A028347, A140090, A014106, A028895, A045944, A186029, A007742, A033429, A022268, A049452, A186030, A135703, A152734, A139273. Cf. similar sequences listed in A254963. Cf. similar sequences listed in A022289. Cf. A060544, A016813. Sequence in context: A234801 A089148 A098319 * A094465 A020580 A172043 Adjacent sequences:  A022264 A022265 A022266 * A022268 A022269 A022270 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified November 26 07:48 EST 2022. Contains 358353 sequences. (Running on oeis4.)