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 A152741 13 times triangular numbers. 4
 0, 13, 39, 78, 130, 195, 273, 364, 468, 585, 715, 858, 1014, 1183, 1365, 1560, 1768, 1989, 2223, 2470, 2730, 3003, 3289, 3588, 3900, 4225, 4563, 4914, 5278, 5655, 6045, 6448, 6864, 7293, 7735, 8190, 8658, 9139, 9633, 10140, 10660, 11193, 11739, 12298, 12870 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Sequence found by reading the line from 0, in the direction 0, 13,... and the same line from 0, in the direction 0, 39,..., in the square spiral whose vertices are the generalized 15-gonal numbers. - Omar E. Pol, Oct 03 2011 Sum of the numbers from 6n to 7n. - Wesley Ivan Hurt, Dec 22 2015 LINKS G. C. Greubel, Table of n, a(n) for n = 0..5000 Index entries for linear recurrences with constant coefficients, signature (3,-3,1). FORMULA a(n) = 13*n*(n+1)/2 = 13 * A000217(n). a(n) = a(n-1)+13*n (with a(0)=0). - Vincenzo Librandi, Nov 26 2010 a(n) = A069126(n+1) - 1. - Omar E. Pol, Oct 03 2011 From Wesley Ivan Hurt, Dec 22 2015: (Start) G.f.: 13*x/(1-x)^3. a(n) = 3*a(n-1)-3*a(n-2)+a(n-3) for n>2. a(n) = Sum_{i=6n..7n} i. (End) E.g.f.: 13*x*(2+x)*exp(x)/2. - G. C. Greubel, Sep 01 2018 MAPLE A152741:=n->13*n*(n+1)/2: seq(A152741(n), n=0..60); # Wesley Ivan Hurt, Dec 22 2015 MATHEMATICA Table[13*n*(n-1)/2, {n, 100}] (* Vladimir Joseph Stephan Orlovsky, Jul 06 2011 *) CoefficientList[Series[13 x/(1 - x)^3, {x, 0, 50}], x] (* Wesley Ivan Hurt, Dec 22 2015 *) PROG (MAGMA) [13*n*(n+1)/2 : n in [0..60]]; // Wesley Ivan Hurt, Dec 22 2015 (PARI) a(n)=13*n*(n+1)/2 \\ Charles R Greathouse IV, Jun 17 2017 CROSSREFS Cf. A000217, A049598, A069126. Sequence in context: A299055 A158647 A283123 * A168235 A258597 A299816 Adjacent sequences:  A152738 A152739 A152740 * A152742 A152743 A152744 KEYWORD easy,nonn AUTHOR Omar E. Pol, Dec 12 2008 STATUS approved

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Last modified February 17 12:29 EST 2020. Contains 331996 sequences. (Running on oeis4.)