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A186029
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a(n) = n*(7*n+3)/2.
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16
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0, 5, 17, 36, 62, 95, 135, 182, 236, 297, 365, 440, 522, 611, 707, 810, 920, 1037, 1161, 1292, 1430, 1575, 1727, 1886, 2052, 2225, 2405, 2592, 2786, 2987, 3195, 3410, 3632, 3861, 4097, 4340, 4590, 4847, 5111, 5382, 5660, 5945, 6237, 6536, 6842, 7155, 7475
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OFFSET
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0,2
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COMMENTS
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This sequence is related to A050409 by A050409(n) = n*a(n) - Sum_{i=0..n-1} a(i).
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LINKS
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FORMULA
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G.f.: x*(5+2*x)/(1-x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>2, a(0)=0, a(1)=5, a(2)=17. - Philippe Deléham, Mar 26 2013
E.g.f.: (1/2)*(7*x^2 + 10*x)*exp(x). - G. C. Greubel, Jul 17 2017
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EXAMPLE
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. n=1 n=2 n=3 n=4
(End)
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MATHEMATICA
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LinearRecurrence[{3, -3, 1}, {0, 5, 17}, 50] (* Harvey P. Dale, Sep 07 2022 *)
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PROG
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(Magma) [n*(7*n+3)/2: n in [0..44]];
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CROSSREFS
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Cf. numbers of the form n*(d*n+10-d)/2 indexed in A140090.
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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