A211013 Second 13-gonal numbers: a(n) = n*(11*n+9)/2.

0, 10, 31, 63, 106, 160, 225, 301, 388, 486, 595, 715, 846, 988, 1141, 1305, 1480, 1666, 1863, 2071, 2290, 2520, 2761, 3013, 3276, 3550, 3835, 4131, 4438, 4756, 5085, 5425, 5776, 6138, 6511, 6895, 7290, 7696, 8113, 8541, 8980, 9430, 9891, 10363

Offset

0,2

Comments

Sequence found by reading the line from 0, in the direction 0, 31... and the line from 10, in the direction 10, 63,..., in the square spiral whose vertices are the generalized 13-gonal numbers A195313.

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

G.f.: x*(10+x)/(1-x)^3. - Philippe Deléham, Mar 27 2013

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) with a(0) = 0, a(1) = 10, a(2) = 31. - Philippe Deléham, Mar 27 2013

a(n) = A051865(n) + 9n = A180223(n) + 8n = A022268(n) + 5n = A022269(n) + 4n = A152740(n) - n. - Philippe Deléham, Mar 27 2013

a(n) = A218530(11n+9). - Philippe Deléham, Mar 27 2013

E.g.f.: x*(20 + 11*x)*exp(x)/2. - G. C. Greubel, Jul 04 2019

Mathematica

Table[n*(11*n+9)/2, {n, 0, 50}] (* G. C. Greubel, Jul 04 2019 *)

Prog

(PARI) a(n)=n*(11*n+9)/2 \\ Charles R Greathouse IV, Jun 17 2017
(Magma) [n*(11*n+9)/2: n in [0..50]]; // G. C. Greubel, Jul 04 2019
(Sage) [n*(11*n+9)/2 for n in (0..50)] # G. C. Greubel, Jul 04 2019
(GAP) List([0..50], n-> n*(11*n+9)/2) # G. C. Greubel, Jul 04 2019

Crossrefs

Bisection of A195313.

Second k-gonal numbers (k=5..14): A005449, A014105, A147875, A045944, A179986, A033954, A062728, A135705, this sequence, A211014.

Cf. A051865.

Sequence in context: A063154 A100500 A209994 * A085473 A051943 A059306

Adjacent sequences: A211010 A211011 A211012 * A211014 A211015 A211016

Keyword

nonn,easy

Author

Omar E. Pol, Aug 04 2012

Status

approved