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A226491 a(n) = n*(21*n-17)/2. 4
0, 2, 25, 69, 134, 220, 327, 455, 604, 774, 965, 1177, 1410, 1664, 1939, 2235, 2552, 2890, 3249, 3629, 4030, 4452, 4895, 5359, 5844, 6350, 6877, 7425, 7994, 8584, 9195, 9827, 10480, 11154, 11849, 12565, 13302, 14060, 14839, 15639, 16460, 17302, 18165, 19049 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Sum of n-th dodecagonal number and n-th tridecagonal number.

Sum of reciprocals of a(n), for n>0: 0.58517199913243139233033474262449...

LINKS

Bruno Berselli, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

FORMULA

G.f.: x*(2+19*x)/(1-x)^3.

a(n) + a(-n) = A064762(n).

MATHEMATICA

Table[n (21 n - 17)/2, {n, 0, 50}]

CoefficientList[Series[x (2 + 19 x) / (1 - x)^3, {x, 0, 45}], x] (* Vincenzo Librandi, Aug 18 2013 *)

PROG

(MAGMA) [n*(21*n-17)/2: n in [0..50]];

(MAGMA) I:=[0, 2, 25]; [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*(21*n-17)/2 \\ Charles R Greathouse IV, Jun 17 2017

CROSSREFS

Cf. A051624, A051865.

Cf. numbers of the form n*(n*k-k+4))/2, this sequence is the case k=21: see list in A226488.

Sequence in context: A038834 A041071 A153478 * A062933 A069232 A269232

Adjacent sequences:  A226488 A226489 A226490 * A226492 A226493 A226494

KEYWORD

nonn,easy

AUTHOR

Bruno Berselli, Jun 09 2013

STATUS

approved

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Last modified October 21 21:46 EDT 2019. Contains 328315 sequences. (Running on oeis4.)