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 A274830 Numbers n such that 7*n+1 is a triangular number (A000217). 4
 0, 2, 5, 11, 17, 27, 36, 50, 62, 80, 95, 117, 135, 161, 182, 212, 236, 270, 297, 335, 365, 407, 440, 486, 522, 572, 611, 665, 707, 765, 810, 872, 920, 986, 1037, 1107, 1161, 1235, 1292, 1370, 1430, 1512, 1575, 1661, 1727, 1817, 1886, 1980, 2052, 2150, 2225 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Colin Barker, Table of n, a(n) for n = 1..1000 Index entries for linear recurrences with constant coefficients, signature (1,2,-2,-1,1). FORMULA G.f.: x^2*(2 + 3*x + 2*x^2) / ((1 - x)^3*(1 + x)^2). a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4) + a(n-5) for n>5. a(n) = (14*(n - 1)*n + (2*n - 1)*(-1)^n + 1)/16. Therefore: a(n) = n*(7*n - 6)/8 for n even, a(n) = (n - 1)*(7*n - 1)/8 for n odd. MATHEMATICA Table[(14 (n - 1) n + (2 n - 1) (-1)^n + 1)/16, {n, 1, 60}] (* Bruno Berselli, Jul 08 2016 *) PROG (PARI) select(n->ispolygonal(7*n+1, 3), vector(3000, n, n-1)) (PARI) concat(0, Vec(x^2*(2+3*x+2*x^2)/((1-x)^3*(1+x)^2) + O(x^100))) CROSSREFS Cf. A000217. Cf. similar sequences where k*n+1 is a triangular number: A000096 (k=1), A074377 (k=2), A045943 (k=3), A274681 (k=4), A085787 (k=5), A274757 (k=6). Sequence in context: A115057 A228344 A157421 * A038390 A048210 A153222 Adjacent sequences: A274827 A274828 A274829 * A274831 A274832 A274833 KEYWORD nonn,easy AUTHOR Colin Barker, Jul 08 2016 EXTENSIONS Edited by Bruno Berselli, Jul 08 2016 STATUS approved

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Last modified May 23 07:28 EDT 2024. Contains 372760 sequences. (Running on oeis4.)