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A226489
a(n) = n*(15*n-11)/2.
5
0, 2, 19, 51, 98, 160, 237, 329, 436, 558, 695, 847, 1014, 1196, 1393, 1605, 1832, 2074, 2331, 2603, 2890, 3192, 3509, 3841, 4188, 4550, 4927, 5319, 5726, 6148, 6585, 7037, 7504, 7986, 8483, 8995, 9522, 10064, 10621, 11193, 11780, 12382, 12999, 13631, 14278, 14940
OFFSET
0,2
COMMENTS
Sum of n-th 9-gonal (nonagonal) number and n-th 10-gonal (decagonal) number.
Sum of reciprocals of a(n), for n > 0: 0.614629940137818703272919217222307...
FORMULA
G.f.: x*(2+13*x)/(1-x)^3.
a(n) + a(-n) = A064761(n).
From Elmo R. Oliveira, Jan 12 2025: (Start)
E.g.f.: exp(x)*x*(4 + 15*x)/2.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2. (End)
MATHEMATICA
Table[n (15 n - 11)/2, {n, 0, 50}]
CoefficientList[Series[x (2 + 13 x) / (1 - x)^3, {x, 0, 45}], x] (* Vincenzo Librandi, Aug 18 2013 *)
PROG
(Magma) [n*(15*n-11)/2: n in [0..50]];
(Magma) I:=[0, 2, 19]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+Self(n-3): n in [1..45]]; // Vincenzo Librandi, Aug 18 2013
(PARI) a(n)=n*(15*n-11)/2 \\ Charles R Greathouse IV, Oct 07 2015
CROSSREFS
Cf. numbers of the form n*(n*k - k + 4)/2, this sequence is the case k=15: see list in A226488.
Sequence in context: A307554 A031911 A136685 * A125201 A215392 A340558
KEYWORD
nonn,easy
AUTHOR
Bruno Berselli, Jun 09 2013
STATUS
approved