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 A005476 a(n) = n*(5*n - 1)/2. 24
 0, 2, 9, 21, 38, 60, 87, 119, 156, 198, 245, 297, 354, 416, 483, 555, 632, 714, 801, 893, 990, 1092, 1199, 1311, 1428, 1550, 1677, 1809, 1946, 2088, 2235, 2387, 2544, 2706, 2873, 3045, 3222, 3404, 3591 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 Leo Tavares, Illustration: Triangulated Diamonds Index entries for linear recurrences with constant coefficients, signature (3,-3,1). FORMULA a(n) = C(5*n,2)/5 for n>=0. - Zerinvary Lajos, Jan 02 2007 a(n) = A033991(n) - A000326(n). - Zerinvary Lajos, Jun 11 2007 a(n) = a(n-1) + 5*n - 3 for n>0, a(0)=0. - Vincenzo Librandi, Nov 18 2010 a(n) = A000217(n) + A000384(n) = A000290(n) + A000326(n). - Omar E. Pol, Jan 11 2013 a(n) = A130520(5*n+1). - Philippe Deléham, Mar 26 2013 a(n) = A033994(n) - A033994(n-1). - J. M. Bergot, Jun 12 2013 From Bruno Berselli, Oct 17 2016: (Start) G.f.: x*(2 + 3*x)/(1 - x)^3. a(n) = A000217(3*n-1) - A000217(2*n-1). (End) E.g.f.: x*(4 + 5*x)*exp(x)/2. - G. C. Greubel, Jul 30 2019 Sum_{n>=1} 1/a(n) = 2 * A294833. - Amiram Eldar, Nov 16 2020 From Leo Tavares, Nov 20 2021: (Start) a(n) = A016754(n) - A133694(n+1). See Triangulated Diamonds illustration. a(n) = A000290(n) + A000217(n) + 2*A000217(n-1) a(n) = 2*A000217(n) + 3*A000217(n-1). (End) MAPLE [seq(binomial(5*n, 2)/5, n=0..40)]; # Zerinvary Lajos, Jan 02 2007 MATHEMATICA Table[n(5n-1)/2, {n, 0, 40}] (* Vladimir Joseph Stephan Orlovsky, Oct 25 2008 *) PROG (PARI) a(n)=n*(5*n-1)/2 \\ Charles R Greathouse IV, Sep 24 2015 (Magma) [Binomial(5*n, 2)/5: n in [0..40]]; // G. C. Greubel, Jul 30 2019 (Sage) [binomial(5*n, 2)/5 for n in (0..40)] # G. C. Greubel, Jul 30 2019 (GAP) List([0..40], n-> Binomial(5*n, 2)/5); # G. C. Greubel, Jul 30 2019 CROSSREFS Cf. A000217, A005475, A033994, A294833. Cf. numbers of the form n*(n*k-k+4))/2 listed in A226488. Cf. similar sequences listed in A022288. Cf. A016754, A133694, A000290. Sequence in context: A002888 A041963 A298912 * A316430 A131476 A023549 Adjacent sequences: A005473 A005474 A005475 * A005477 A005478 A005479 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified December 7 19:19 EST 2022. Contains 358669 sequences. (Running on oeis4.)