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A152741
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13 times triangular numbers.
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4
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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
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OFFSET
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0,2
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COMMENTS
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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
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LINKS
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G. C. Greubel, Table of n, a(n) for n = 0..5000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
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FORMULA
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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
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MAPLE
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A152741:=n->13*n*(n+1)/2: seq(A152741(n), n=0..60); # Wesley Ivan Hurt, Dec 22 2015
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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Cf. A000217, A049598, A069126.
Sequence in context: A299055 A158647 A283123 * A168235 A258597 A299816
Adjacent sequences: A152738 A152739 A152740 * A152742 A152743 A152744
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KEYWORD
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easy,nonn
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AUTHOR
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Omar E. Pol, Dec 12 2008
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STATUS
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approved
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